Artykuły w czasopismach na temat „Non-harmonic Fourier series”
Kliknij ten link, aby zobaczyć inne rodzaje publikacji na ten temat: Non-harmonic Fourier series.
Utwórz poprawne odniesienie w stylach APA, MLA, Chicago, Harvard i wielu innych
Sprawdź 50 najlepszych artykułów w czasopismach naukowych na temat „Non-harmonic Fourier series”.
Przycisk „Dodaj do bibliografii” jest dostępny obok każdej pracy w bibliografii. Użyj go – a my automatycznie utworzymy odniesienie bibliograficzne do wybranej pracy w stylu cytowania, którego potrzebujesz: APA, MLA, Harvard, Chicago, Vancouver itp.
Możesz również pobrać pełny tekst publikacji naukowej w formacie „.pdf” i przeczytać adnotację do pracy online, jeśli odpowiednie parametry są dostępne w metadanych.
Przeglądaj artykuły w czasopismach z różnych dziedzin i twórz odpowiednie bibliografie.
1
Sedletskii, A. M. "On the summability and convergence of non-harmonic Fourier series". Izvestiya: Mathematics 64, nr 3 (30.06.2000): 583–600. http://dx.doi.org/10.1070/im2000v064n03abeh000292.
Pełny tekst źródła
2
NIKOLAEV, NIKOLAY Y., i HITOSHI IBA. "GENETIC PROGRAMMING OF POLYNOMIAL HARMONIC NETWORKS USING THE DISCRETE FOURIER TRANSFORM". International Journal of Neural Systems 12, nr 05 (październik 2002): 399–410. http://dx.doi.org/10.1142/s0129065702001242.
Pełny tekst źródłaStreszczenie:
This paper presents a genetic programming system that evolves polynomial harmonic networks. These are multilayer feed-forward neural networks with polynomial activation functions. The novel hybrids assume that harmonics with non-multiple frequencies may enter as inputs the activation polynomials. The harmonics with non-multiple, irregular frequencies are derived analytically using the discrete Fourier transform. The polynomial harmonic networks have tree-structured topology which makes them especially suitable for evolutionary structural search. Empirical results show that this hybrid genetic programming system outperforms an evolutionary system manipulating polynomials, the traditional Koza-style genetic programming, and the harmonic GMDH network algorithm on processing time series.
3
BRINGMANN, KATHRIN, i OLAV K. RICHTER. "EXACT FORMULAS FOR COEFFICIENTS OF JACOBI FORMS". International Journal of Number Theory 07, nr 03 (maj 2011): 825–33. http://dx.doi.org/10.1142/s1793042111004617.
Pełny tekst źródłaStreszczenie:
In previous work, we introduced harmonic Maass–Jacobi forms. The space of such forms includes the classical Jacobi forms and certain Maass–Jacobi–Poincaré series, as well as Zwegers' real-analytic Jacobi forms, which play an important role in the study of mock theta functions and related objects. Harmonic Maass–Jacobi forms decompose naturally into holomorphic and non-holomorphic parts. In this paper, we give exact formulas for the Fourier coefficients of the holomorphic parts of harmonic Maass–Jacobi forms and, in particular, we obtain explicit formulas for the Fourier coefficients of weak Jacobi forms.
4
Strizhkov, I. G., E. N. Chesnyuk i R. B. Goldman. "Harmonic Analysis of Non-sinusoidal Currents During Heating of Transformers". Machinery and Equipment for Rural Area, nr 8 (27.08.2023): 40–42. http://dx.doi.org/10.33267/2072-9642-2023-8-40-42.
Pełny tekst źródłaStreszczenie:
The results of the analysis of currents in the transformer windings when heated by low-frequency short-circuit currents are presented, for the description of which the Fourier series expansion of piecewise exponential functions is used. This makes it possible to mathematically model the heating process and solve the issues of the ratio of the power released in the electric and magnetic circuits of the transformer.
5
Nigmatullin, Raoul R., Airat A. Khamzin i Yangquan Chen. "Approximation of Aperiodic Signals Using Non-Integer Harmonic Series: The Generalized NAFASS Approach". Fractal and Fractional 7, nr 7 (23.06.2023): 498. http://dx.doi.org/10.3390/fractalfract7070498.
Pełny tekst źródłaStreszczenie:
In this paper, the non-orthogonal amplitude-frequency analysis of smoothed signals (NAFASS) method) is used to approximate discrete aperiodic signals from various complex systems with the non-integer harmonic series (NIHS). When approximating by the NIHS, there is a problem in determining the dispersion law for harmonic frequencies. In the original version of the NAFASS approach, the frequency dispersion law was determined from a linear-difference equation. However, many complex systems in nature have frequency distributions that differ from the linear law, which is used in the conventional Fourier analysis of periodic signals. This paper proposes a generalization of the NAFASS method for describing aperiodic signals by the NIHS with a frequency distribution that satisfies a recursive formula, which coincides with the local generalized geometric mean (GGM). The methodology of the generalized NAFASS method is demonstrated using descriptions of financial data (prices for metals) and sound data (sounds of insects) as examples. The results show the effectiveness of the generalized NAFASS approach for describing real-world time data. This discovery allows us to propose a new classification scheme for smoothed and aperiodic signals captured as responses and envelopes from various complex systems.
6
Osipov, Vyacheslav S. "Method of calculating the distortion coefficient sinusoidality of the voltage curve created by three-phase straight lines". Vestnik of Samara State Technical University. Technical Sciences Series 29, nr 4 (15.12.2021): 99–115. http://dx.doi.org/10.14498/tech.2021.4.8.
Pełny tekst źródłaStreszczenie:
The existing calculation methods in various sources represent rectifier installations as sources of higher harmonics. In this case, the current value of the primary winding of the transformer in the form of rectangles is decomposed into a Fourier series and harmonic components of the current are obtained, except for the main harmonic higher 5, 7, 11, 13, 17, 19 The amplitudes of the current of the higher harmonics are multiplied by the inductive resistances of the supply network corresponding to the frequencies, the results are squared and summed up. Obviously, all terms are of equal magnitude, since with an increase in the harmonic number, its amplitude decreases by n times compared to the first harmonic, while the frequency and inductive resistance increase by the same number of times. The non-sinusoidal coefficient Ku is defined as the ratio of the square root of the sum to the magnitude of the phase voltage. The disadvantage of determining Ku is some arbitrariness in the number of harmonics taken into account. If we take, for example, 9 harmonics, we get Ku = 7.22%, if 4 harmonics, then Ku = 4.81%. When the current of the primary winding of the transformer flows, the voltage amplitude on the substation tires decreases by only 1.9 V. At the same time, the coefficient of non-sinusoidality cannot be equal to 7.22%. In all literature sources, when calculating current harmonics, there are no recommendations for which harmonic numbers should be installed at the substation resonant filters. It is no coincidence that in the new GOST-2013, the value of the distortion coefficient of the sinusoidal voltage curve K(U is calculated as a percentage as a result of the i-th observation according to the formula, (that is, no calculation is made by current harmonics). In this paper, another approach is made to determine the distortion coefficient of the sinusoidal voltage curve. Rectifier installations are not sources of harmonics, but are electrical receivers with a nonlinear characteristic of electric current consumption, while the shape of the sinusoid curve of the supply voltage is distorted. This distorted sine wave is the source of the higher harmonics, which in this paper is decomposed into a Fourier series, while the calculation of the integral functions of the coefficients of the Fourier series is performed in the Mathcad program. The solution is made for three rectifier circuits. Harmonics for the installation of resonant filters are determined. As a result, a developed method is proposed for calculating the higher voltage harmonics and determining the distortion coefficient of the sinusoidal voltage curve based on the Fourier series expansion of the distorted voltage sine curve during operation of three-phase uncontrolled rectifiers.
7
Leblanc, Jean L., i Christophe de la Chapelle. "Characterizing Gum Elastomers by Fourier Transform Rheometry". Rubber Chemistry and Technology 76, nr 4 (1.09.2003): 979–1000. http://dx.doi.org/10.5254/1.3547786.
Pełny tekst źródłaStreszczenie:
Abstract Fourier transform (FT) rheometry is an emerging new technique that allows the linear and non-linear viscoelastic behavior of polymer materials to be accurately investigated. Basically samples are submitted to torsional harmonic strain at fixed frequency and temperature in order to capture strain and torque signals. A commercial instrument, i.e. the Rubber Process Analyzer RPA 2000® (Alpha Technologies), was suitably modified, essentially in using a fast electronic analogic-digital conversion card to record and treat torque and strain signals using purposely written software. Details of such modifications were previously published and the work presented is a sequel of this development. The quality of the applied strain is first precisely documented through FT and found excellent, particularly in the high strain range. Three gum EPDM with different macromolecular characteristics (MWD and long chain branching) were analyzed either using standard dynamic testing, i.e. essentially in the linear viscoelastic range, or using the Fourier transform rheometry approach, by considering data gathered in the far non-linear viscoelastic range. Data obtained are considered with respect to know features of the samples. A series of SBR 1500 samples, collected from various manufacturers, were first analyzed using standard methods; as expected very small differences were seen. Then FT was used to consider torque signals at very high strain (up to 400% at 1 Hz). Using a simple 4-parameter model to treat the variation upon increasing strain of the relative third harmonic component of the torque signal, differences are clearly detected that are discussed with respect to available polymer manufacturing information.
8
Qi, Hui, Gen Chang Zhang i Jing Fu Nan. "Ground Motion of Non-Circular Alluvial Valley for Incident Plane SH-Wave". Applied Mechanics and Materials 105-107 (wrzesień 2011): 2092–97. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.2092.
Pełny tekst źródłaStreszczenie:
The seismic ground motions are studied in an infinite half-space with a non-circular alluvial valley under time harmonic incident anti-plane shear waves. Based on the conformal mapping method and Fourier series expansions, the conditions of displacement continuity and stress equilibrium at the interface of alluvial valley are set as semi-circular alluvial valley in conformal plane, then the result is obtained by constructing a set of infinite linear algebraic equations with boundary discretization. The unknown coefficients in the algebraic system can be easily determined. The present method is treated as a semi-analytical solution since error only attributes to the truncation of Fourier series. Earthquake analysis for the site response of alluvial valley or canyon subject to the incident SH-wave is the main concern. Numerical examples for semi-elliptic alluvial valley are given to test our program. The research indicates that great interaction exists between the alluvial valley and the horizontal surface, which will bring on great influence on ground motion. Therefore enough importance must be attached to the existing of subsurface cavity while finishing seismic design.
9
Lindberg, Anders, Bo Lövgren, Jennie Asp, Jérôme Antoni i Andreas Gällström. "Short-time least squares spectral analysis of pass-by noise in water from a rigid inflatable boat". Journal of the Acoustical Society of America 151, nr 3 (marzec 2022): 1932–43. http://dx.doi.org/10.1121/10.0009847.
Pełny tekst źródłaStreszczenie:
This paper investigates least squares spectral analysis as a tool to analyze non-stationary signals from pass-by noise measurements in water. The spectral analysis involves successive least squares fitting of a finite Fourier series to approximate the observation in a piecewise manner. The least squares spectral analysis is used to search the signals for first- and second-order periodicity as well as the presence of fundamental periodicity. A first-order analysis reveals line components in the signals, whereas a second-order analysis reveals periodic amplitude modulations. Analysis with a higher-order finite Fourier series reveals harmonic structures in the signals. The main contribution of this paper is the model of a magnitude-squared cosine wave which can be used to analyze second-order periodicity. The developed short-time least squares spectral analysis is illustrated on noise radiated from a rigid inflatable boat in shallow water.
10
Sinou, Jean Jacques. "Analysis of the Response of a Rotor System Containing a Breathing Crack". Key Engineering Materials 413-414 (czerwiec 2009): 479–86. http://dx.doi.org/10.4028/www.scientific.net/kem.413-414.479.
Pełny tekst źródłaStreszczenie:
The purpose of this paper is to investigate the influence of the presence of transverse cracks in rotors. The dynamic response of the cracked rotor is evaluated by expanding the changing stiffness of the crack (i.e. the breathing mechanism) as a truncated Fourier series and then using the Harmonic Balance Method. The crack detection is based on the use of the 2X and 3X super-harmonic frequency components of the non-linear dynamical behaviour at the associated sub-critical resonant peaks. Various parametric studies including the effects of the crack depth and location, and the crack–unbalance interaction on the dynamic of a crack rotor are undertaken. It will be illustrated that the emerging of super-harmonic frequency components and/or antiresonances can provide useful information on the presence of cracks and may be used on an on-line crack monitoring rotor system for small levels of damage.
11
Witczak, Pawel, Witold Kubiak, Marcin Lefik i Jacek Szulakowski. "Modal-frequency spectrum of magnetic flux density in air gap of permanent magnet motor". Archives of Electrical Engineering 63, nr 1 (1.03.2014): 29–46. http://dx.doi.org/10.2478/aee-2014-0003.
Pełny tekst źródłaStreszczenie:
Abstract The classic relationships concerning the harmonic content in the air gap field of three-phase machines are presented in form of series of rotating waves. The same approach is applied to modeling of permanent magnet motors with fractional phase windings. All main reasons of non-sinusoidal shape of flux density distribution, namely, magnets’ shape and their placement, slotting, magnetic saturation and eccentricity are also related to their counterparts in modal-frequency spectrum. The Fourier 2D spectrum of time-stepping finite element solution is confronted with results of measurements, with special attention paid to accuracy of both methods
12
Bulgakov, V., V. Melnik, A. F. M. A. Mohammed, M. Korenko i K. Kollárová. "Methodology of processing the results of field experiment monitoring of the technological procedure of sowing". Research in Agricultural Engineering 62, No. 1 (30.03.2016): 30–36. http://dx.doi.org/10.17221/8/2015-rae.
Pełny tekst źródłaStreszczenie:
The non-uniformity of distribution of seeds sown in a row influences their productivity. To analyse and eliminate the causes of non-uniformities, the straight motion of coulters must be separated from generation of causes, i.e. the deviation of seeds from an ideal position on the coulter trajectory. A partial acceleration method can be effectively used to recover the coulter trajectory. It is based on the study of machine parts dynamics by measuring the three-dimensional projection of acceleration and its characteristic points. Fourier methods are used for approximation or interpolation of experimental data. The trajectory of a point is obtained by double integration of a Fourier series. Noise generation in acceleration measurement can be solved by smoothing with reasonable intensity. Also double integration leads to smoothing, the variability of the number of points participates in assessing the degree of harmonic distortion of reconstructed trajectory, based on which the required smoothing limit can be set. The method may be used for monitoring the farm machines dynamics based on the partial acceleration method.
13
Bae, Sungryong, i Pilkee Kim. "Load Resistance Optimization of Bi-Stable Electromagnetic Energy Harvester Based on Harmonic Balance". Sensors 21, nr 4 (22.02.2021): 1505. http://dx.doi.org/10.3390/s21041505.
Pełny tekst źródłaStreszczenie:
In this study, a semi-analytic approach to optimizing the external load resistance of a bi-stable electromagnetic energy harvester is presented based on the harmonic balance method. The harmonic balance analyses for the primary harmonic (period-1T) and two subharmonic (period-3T and 5T) interwell motions of the energy harvester are performed with the Fourier series solutions of the individual motions determined by spectral analyses. For each motion, an optimization problem for maximizing the output power of the energy harvester is formulated based on the harmonic balance solutions and then solved to estimate the optimal external load resistance. The results of a parametric study show that the optimal load resistance significantly depends on the inductive reactance and internal resistance of a solenoid coil––the higher the oscillation frequency of an interwell motion (or the larger the inductance of the coil) is, the larger the optimal load resistance. In particular, when the frequency of the ambient vibration source is relatively high, the non-linear dynamic characteristics of an interwell motion should be considered in the optimization process of the electromagnetic energy harvester. Compared with conventional resistance-matching techniques, the proposed semi-analytic approach could provide a more accurate estimation of the external load resistance.
14
Khmelnуtskyi, Evgen, i Oleg Klyuyev. "DETERMINATION OF ABNORMAL HARMONICS AND HARMONIC COMPOSITION COEFFICIENTS OF NON-SINUSOIDITY IN A 10 kV NETWORK WITH A VALVE ELECTRIC DRIVE OF DIRECT CURRENT". Collection of scholarly papers of Dniprovsk State Technical University (Technical Sciences) 1, nr (42) (22.05.2023): 128–33. http://dx.doi.org/10.31319/2519-2884.42.2023.15.
Pełny tekst źródłaStreszczenie:
The operation process of the electric valve drive is accompanied by the generation of higher harmonics — canonical and non-canonical. Limitation of the level of canonical harmonics is carried out by power resonance filters, however, in the case of asymmetry of the control pulses of the thyristors of the converters, non-canonical harmonics are generated — both even and odd harmonics. The composition of non-canonical harmonics can be determined in the case of harmonic analysis of non-sinusoidal current and voltage coefficients. The conducted harmonic analysis makes it possible to determine the composition of the filter-compensating device in the case of its design.
The article examines the operation of a power supply unit with a powerful valve electric drive powered by controlled six-phase converters. Experimental measurement of higher harmonics showed the following: canonical harmonics ν £ 13 do not exceed 1—1.5 %, while the non-sinusoidal voltage coefficient exceeds the standard by 5 % (equal to 5.5—8.2 %). Such a situation is possible in the presence of high-order abnormal harmonics, which can be explained by the asymmetry of thyristor opening pulses e ³ 3 el. deg.
This study is devoted to the analysis of the operation of the power supply unit with a powerful DC valve electric drive powered by controlled six-phase converters. Measurements showed an insignificant level of canonical harmonics (up to 1.5 %), while harmonics ν = 21—39 exceeded 2.5—3.5 %. Such a situation can be explained by the presence of abnormal harmonics of a high order, when the asymmetry of the opening pulses of the thyristors of the converters exceeds 3 el. deg. The analysis of the non-sinusoidal coefficients as a random process and its decomposition into a Fourier series made it possible to determine the harmonic composition of the current and voltage non-sinusoidal coefficients. Thus, the task of the research is defined in the calculation of the harmonic composition of non-sinusoidal coefficients and the analysis of abnormal harmonics
15
Axelsson, Owe, i Dalibor Lukáš. "Preconditioning methods for eddy-current optimally controlled time-harmonic electromagnetic problems". Journal of Numerical Mathematics 27, nr 1 (26.03.2019): 1–21. http://dx.doi.org/10.1515/jnma-2017-0064.
Pełny tekst źródłaStreszczenie:
Abstract Time-harmonic problems arise in many important applications, such as eddy current optimally controlled electromagnetic problems. Eddy current modelling can also be used in non-destructive testings of conducting materials. Using a truncated Fourier series to approximate the solution, for linear problems the equation for different frequencies separate, so it suffices to study solution methods for the problem for a single frequency. The arising discretized system takes a two-by-two or four-by-four block matrix form. Since the problems are in general three-dimensional in space and hence of very large scale, one must use an iterative solution method. It is then crucial to construct efficient preconditioners. It is shown that an earlier used preconditioner for optimal control problems is applicable here also and leads to very tight eigenvalue bounds and hence very fast convergence such as for a Krylov subspace iterative solution method. A comparison is done with an earlier used block diagonal preconditioner.
16
Park, S. G., i B. M. Kwak. "A Semi-Analytical Finite Element Method for Three-Dimensional Contact Problems with Axisymmetric Geometry". Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 200, nr 6 (listopad 1986): 399–405. http://dx.doi.org/10.1243/pime_proc_1986_200_148_02.
Pełny tekst źródłaStreszczenie:
A combination of conventional two-dimensional finite elements and a Fourier series expansion in the tangential direction is shown to be efficient for modelling an elastic three-dimensional frictionless contact problem of geometrically axisymmetric bodies under non-axisymmetric external loads. For the solution procedure, the governing partial differential equations and contact conditions on the contact surface are formulated into an equivalent minimization problem with constraints. It is shown that the resulting objective function can be expressed as the sum of decoupled contributions from each harmonic. A modified simplex method is used to solve this quadratic programming problem. An example problem, motivated from a modular prosthesis design for artificial joint replacements, has shown the significant computational efficiency of this approach as compared to a conventional full three-dimensional finite element method.
17
Pascal, R., P. Conraux i J. M. Bergheau. "A new method for the numerical simulation of induction hardening processes". Journal de Physique IV 120 (grudzień 2004): 337–45. http://dx.doi.org/10.1051/jp4:2004120038.
Pełny tekst źródłaStreszczenie:
Numerical simulation of induction heating operations rests on the modelling of coupled non-linear thermal and magnetodynamic analyses. Strong couplings come from, on one hand, the power dissipated through Joule effect, and on the other hand, electromagnetic properties that depend on temperature. Usually, an indirect or staggered method is used to solve such problems. Several magnetodynamic and thermal simulations are therefore performed alternatively and sequentially. This paper presents a new method solving thermo-metallurgical and magnetodynamic problems together and based on the harmonic balance finite element formulation (HBFEM) of the electromagnetic problem. The temperature and the different harmonics of the Fourier series of the unknown electromagnetic variables are now calculated in a same finite element. An example of the numerical simulation of an induction hardening process is presented. The results obtained with different approaches are compared.
18
Jerkan, Dejan, i Darko Marčetić. "Advanced model of IM including rotor slot harmonics". COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 34, nr 1 (5.01.2015): 261–78. http://dx.doi.org/10.1108/compel-03-2014-0051.
Pełny tekst źródłaStreszczenie:
Purpose – The purpose of this paper is to present a detailed advanced dynamical model of induction machine (IM) with unskewed rotor bars, including rotor slot harmonics. Design/methodology/approach – Procedure of IM modeling using results from finite element analysis (FEA). Series of magneto-static FEA simulations are used to obtain matrix of IM inductances as a function of rotor angular position and geometry. Each element in this matrix is represented by Fourier series (FS) and incorporated in proposed dynamical model. Using or neglecting various elements in FS of inductance matrix may be useful for determining which component of the series has dominant influence on harmonic content of stator currents, torque ripple or speed variation. The usefulness of application of presented model is verified comparing with time-stepping FEA simulations. Findings – Although the model is not suitable for usage in on-line regulation of IM drives, but the results of simulations may be used to thoroughly explain origins of higher order harmonics in stator currents of IM and help improve sensorless speed estimation algorithms and fault diagnostics. Originality/value – This paper shows an approach to the modeling of IM which includes effects of non-uniform air gap and non-sinusoidal distributions of magneto-motive forces. Inductance matrix elements are complex functions of rotor position, geometry and winding distributions and it gives an opportunity for detail analysis of IM behavior in numerous applications.
19
Kolyanova, A. S. "Restoration of the orientation distribution function for materials with low lattice and sample symmetry using the harmonic method". Industrial laboratory. Diagnostics of materials 89, nr 9 (24.09.2023): 34–40. http://dx.doi.org/10.26896/1028-6861-2023-89-9-34-40.
Pełny tekst źródłaStreszczenie:
A lot of the properties polycrystalline materials depend on their crystallographic texture. The most complete information about the texture can be obtained from the orientation distribution function (ODF). We present the results of recovering ODF using series expansion technique for materials with low crystal and sample symmetry. The technique of ODF restoration is based on its Fourier series expansion with symmetrical spherical harmonic functions. Real spherical harmonics which are linear combinations of general spherical harmonics were used. The model single-component texture as well as the real texture of magnesium alloy sample subjected to equal-channel angular pressing have been studied. Textures are characterized by hexagonal crystal symmetry and triclinic sample symmetry. In both cases RP-factors and ODF calculation errors that were used as reliability criteria of ODF reconstruction showed good agreement between the calculated and experimental data. It was also revealed that the ODF of a magnesium alloy sample subjected to equal-channel angular pressing contains two texture components (1216)[1211] and (1216)[1211] with maximum intensity values of 13.81 and 2.23, respectively. The results obtained can be used for texture studies of ceramics, rocks and other non-metallic materials characterized by a lower symmetry.
20
Gudmestad, Ove Tobias. "Resonant Motions of Dynamic Offshore Structures in Large Waves". Fluids 6, nr 10 (7.10.2021): 352. http://dx.doi.org/10.3390/fluids6100352.
Pełny tekst źródłaStreszczenie:
In marine engineering, the dynamics of fixed offshore structures (for oil and gas production or for wind turbines) are normally found by modelling of the motion by a classical mass-spring damped system. On slender offshore structures, the loading due to waves is normally calculated by applying a force which consists of two parts: a linear “inertia/mass force” and a non-linear “drag force” that is proportional to the square of the velocity of the particles in the wave, multiplied by the direction of the wave particle motion. This is the so-called Morison load model. The loading function can be expanded in a Fourier series, and the drag force contribution exhibits higher order harmonic loading terms, potentially in resonance with the natural frequencies of the system. Currents are implemented as constant velocity terms in the loading function. The paper highlights the motion of structures due to non-linear resonant motion in an offshore environment with high wave intensity. It is shown that “burst”/“ringing” type motions could be triggered by the drag force during resonance situations.
21
Кладченко, Ірина. "ПРОГНОЗУВАННЯ ТРАЄКТОРІЇ НАЦІОНАЛЬНОГО ЕКОНОМІЧНОГО РОЗВИТКУ МЕТОДАМИ ГАРМОНІЙНОГО І СПЕКТРАЛЬНОГО АНАЛІЗУ". Economical 1, nr 1(22) (2020): 115–31. http://dx.doi.org/10.31474/1680-0044-2020-1(22)-115-131.
Pełny tekst źródłaStreszczenie:
Improving of the methodological tools for the national economies behavior’s forecasting in the context of increasing the validity and analytical characteristics of state economic strategies in conditions of high volatility, lack of trend stability and non-stationary dynamics of external and internal socio-economic processes by implementing interdisciplinary methods of Fourier analysis and their adaptation to the specifics of the socio-economic systems’ functioning and development. Methodology. The forecasting’s targeting as an important independent stage in the process of analytical assessment of the balance of development is performed on the basis of structuring, division into stages, systematization, and grouping. Justification of the interdisciplinary approach for forecasting of national economic system’s development is carried out by methods of analysis and synthesis, comparison and practical testing. Establishment of the economic dynamics’ structural regularities and forecasting of a trajectory of national economy development are executed by harmonic and spectral analysis of the dynamic systems’ fluctuating processes. The results. The paper’s attention is focused on the specific features of macroeconomic dynamics’ time series as a basis for the forecasting of national economies development, namely their short duration, non-stationary, aperiodic, polyharmonic and their impact on the formation of adequate methodological support for forecasting. The possibility and efficiency of spectral and harmonic methods using for analysis oscillating processes of national economic system’s development are substantiated. A harmonic model of Ukraine's economic development’s trajectory during 1991-2020 is formed, which allowed to analyze the fluctuating component of the macroeconomic indicators’ dynamics on the basis of actual data that included all the initial information contained in the time series. By distinguishing economic cycles, their amplitude-frequency characteristics, the current phase of Ukrainian economy’s development is characterized. On the basis of the economic dynamics’ model, being used the indicator of annual GDP growth, forecasting is executed and short-term, average-term and long-term tendencies Ukraine’s economy’s development are established. Scientific novelty. The extending of theoretical and methodological tools for forecasting of main trends in national economies, based on harmonic and spectral analysis, is allowed to form a structural approach to the analysis of economic dynamics in the context of selection of its decisive harmonics and basing on their characteristics to make conclusions about the current level and projected national economic systems’ development. Practical significance. The adapted and regulated procedure of harmonic and spectral analysis of socio-economic systems’ oscillating processes became the basis for forecasting the level, rates and proportions of national economic systems development.
22
Lee, Sang Hun, Takao Endo i Ryutaro Kawana. "The Effect of Wave Propagation on Seismic Response at Transmitting Boundary of Discrete System". Applied Mechanics and Materials 878 (luty 2018): 110–14. http://dx.doi.org/10.4028/www.scientific.net/amm.878.110.
Pełny tekst źródłaStreszczenie:
When analyzing the seismic response of a very long elevated structure such as a Shinkansen viaduct, it is common practice to analyze a cutout of the structure under consideration and treat its both ends as free boundaries. This is attributable to the assumption that seismic response analysis assuming free boundary conditions is more conservative than one assuming non-free boundary conditions. In this study, after finding out that response to harmonic ground motion can be greater than under free-boundary conditions if outward energy dissipation occurs from the analysis domain, a series of numerical experiments was performed to determine whether such phenomena occur in seismic response. Then, after confirming that the frequency components of ground motion that satisfy the wave propagation condition greatly affect seismic response, the study showed that the area of the wave propagation condition region of the Fourier spectrum can be used as an indicator by which to judge the likelihood of occurrence of such phenomena.
23
Abdul-Rahman, Anmar, William Morgan, Ying Jo Khoo, Christopher Lind, Allan Kermode, William Carroll i Dao-Yi Yu. "Linear interactions between intraocular, intracranial pressure, and retinal vascular pulse amplitude in the fourier domain". PLOS ONE 17, nr 6 (28.06.2022): e0270557. http://dx.doi.org/10.1371/journal.pone.0270557.
Pełny tekst źródłaStreszczenie:
Purpose To compare the retinal vascular pulsatile characteristics in subjects with normal (ICPn) and high (ICPh) intracranial pressure and quantify the interactions between intraocular pressure, intracranial pressure, and retinal vascular pulse amplitude in the Fourier domain. Materials and methods Twenty-one subjects were examined using modified photoplethysmography with simultaneous ophthalmodynamometry. A harmonic regression model was fitted to each pixel in the time-series, and used to quantify the retinal vascular pulse wave parameters including the harmonic regression wave amplitude (HRWa). The pulse wave attenuation was measured under different ranges of induced intraocular pressure (IOPi), as a function of distance along the vessel (VDist). Intracranial pressure (ICP) was measured using lumbar puncture. A linear mixed-effects model was used to estimate the correlations between the Yeo-Johnson transformed harmonic regression wave amplitude (HRWa-YJt) with the predictors (IOPi, VDist and ICP). A comparison of the model coefficients was done by calculating the weighted Beta (βx) coefficients. Results The median HRWa in the ICPn group was higher in the retinal veins (4.563, interquartile range (IQR) = 3.656) compared to the retinal arteries (3.475, IQR = 2.458), p<0.0001. In contrast, the ICPh group demonstrated a reduction in the median venous HRWa (3.655, IQR = 3.223) and an elevation in the median arterial HRWa (3.616, IQR = 2.715), p<0.0001. Interactions of the pulsation amplitude with ICP showed a significant disordinal interaction and the loss of a main effect of the Fourier sine coefficient (bn1) in the ICPh group, suggesting that this coefficient reflects the retinal vascular response to ICP wave. The linear mixed-effects model (LME) showed the decay in the venous (HRWa-YJt) was almost twice that in the retinal arteries (−0.067±0.002 compared to −0.028±0.0021 respectively, p<0.00001). The overall interaction models had a total explanatory power of (conditional R2) 38.7%, and 42% of which the fixed effects explained 8.8%, and 5.8% of the variance (marginal R2) for the venous and arterial models respectively. A comparison of the damping effect of VDist and ICP showed that ICP had less influence on pulse decay than distance in the retinal arteries (βICP = -0.21, se = ±0.017 compared to βVDist=-0.26, se = ±0.019), whereas the mean value was equal for the retinal veins (venous βVDist=-0.42, se = ±0.015, βICP = -0.42, se = ±0.019). Conclusion The retinal vascular pulsation characteristics in the ICPh group showed high retinal arterial and low venous pulsation amplitudes. Interactions between retinal vascular pulsation amplitude and ICP suggest that the Fourier sine coefficient bn1 reflects the retinal vascular response to the ICP wave. Although a matrix of regression lines showed high linear characteristics, the low model explanatory power precludes its use as a predictor of ICP. These results may guide future predictive modelling in non-invasive estimation of ICP using modified photoplethysmography.
24
Zikkos, Elias. "MOMENT PROBLEMS IN WEIGHTED \(L^2\) SPACES ON THE REAL LINE". Ural Mathematical Journal 6, nr 1 (29.07.2020): 168. http://dx.doi.org/10.15826/umj.2020.1.014.
Pełny tekst źródłaStreszczenie:
For a class of sets with multiple terms$$ \{\lambda_n,\mu_n\}_{n=1}^{\infty}:=\{\underbrace{\lambda_1,\lambda_1,\dots,\lambda_1}_{\mu_1 - times},\underbrace{\lambda_2,\lambda_2,\dots,\lambda_2}_{\mu_2 - times},\dots,\underbrace{\lambda_k,\lambda_k,\dots,\lambda_k}_{\mu_k - times},\dots\},$$having density \(d\) counting multiplicities, and a doubly-indexed sequence of non-zero complex numbers\linebr eak \(\{d_{n,k}:\, n\in\mathbb{N},\, k=0,1,\dots ,\mu_n-1\} \) satisfying certain growth conditions, we consider a moment problem of the form $$\int_{-\infty}^{\infty}e^{-2w(t)}t^k e^{\lambda_n t}f(t)\, dt=d_{n,k},\quad \forall\,\, n\in\mathbb{N}\quad \text{and}\quad k=0,1,2,\dots, \mu_n-1,$$ in weighted \(L^2 (-\infty, \infty)\) spaces. We obtain a solution \(f\) which extends analytically as an entire function, admitting a Taylor–Dirichlet series representation $$ f(z)=\sum_{n=1}^{\infty}\Big(\sum_{k=0}^{\mu_n-1}c_{n,k} z^k\Big) e^{\lambda_n z},\quad c_{n,k}\in \mathbb{C},\quad\forall\,\, z\in \mathbb{C}. $$ The proof depends on our previous work where we characterized the closed span of the exponential system \(\{t^k e^{\lambda_n t}:\, n\in\mathbb{N},\,\, k=0,1,2,\dots,\mu_n-1\}\) in weighted \(L^2 (-\infty, \infty)\) spaces, and also derived a sharp upper bound for the norm of elements of a biorthogonal sequence to the exponential system. The proof also utilizes notions from Non-Harmonic Fourier series such as Bessel and Riesz–Fischer sequences.
25
Ranganai, Edmore, i Mphiliseni B. Nzuza. "A comparative study of the stochastic models and harmonically coupled stochastic models in the analysis and forecasting of solar radiation data". Journal of Energy in Southern Africa 26, nr 1 (23.03.2015): 125–37. http://dx.doi.org/10.17159/2413-3051/2015/v26i1a2215.
Pełny tekst źródłaStreszczenie:
Extra-terrestrially, there is no stochasticity in the solar irradiance, hence deterministic models are often used to model this data. At ground level, the Box-Jenkins Seasonal/Non-seasonal Autoregressive Integrated Moving Average (S/ARIMA) short memory stochastic models have been used to model such data with some degree of success. This success is attributable to its ability to capture the stochastic component of the irradiance series due to the effects of the ever-changing atmospheric conditions. However, irradiance data recorded at the earth’s surface is rarely entirely stochastic but a mixture of both deterministic and stochastic components. One plausible modelling procedure is to couple sinusoidal predictors at determined harmonic (Fourier) frequencies to capture the inherent periodicities (seasonalities) due to the diurnal cycle, with SARIMA models capturing the stochastic components. We construct such models which we term, harmonically coupled SARIMA (HCSARIMA) models and use them to empirically model the global horizontal irradiance (GHI) recorded at the earth’s surface. Comparison of the two classes of models shows that HCSARIMA models generally out-compete SARIMA models in the forecasting arena.
26
Andrés, Víctor, Jose Martínez-Casas, Javier Carballeira i Francisco Denia. "Development of a dynamic model of the axisymmetric railway wheel for sound radiation prediction". INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, nr 3 (1.08.2021): 3362–68. http://dx.doi.org/10.3397/in-2021-2385.
Pełny tekst źródłaStreszczenie:
In this work, a vibroacoustic model is developed to predict the dynamic response and sound radiation of an axisymmetric railway wheel under a non-axisymmetric excitation. To do this, first, the energy equation of the wheel is analytically integrated along the circumferential direction after an expansion of its response as Fourier series. Then, the vibrational dynamics of the three-dimensional wheel is solved through a set of two-dimensional problems which come from that integration. Subsequently, the three-dimensional sound radiation of the railway wheel is calculated from the solution of the aforementioned two-dimensional problems by means of analytical relations based on the harmonic distribution of the dynamics in the circumferential coordinate. Additionally, the wheel rotation is introduced in the model using an eulerian approach, in order to consider the associated gyroscopic and inertial effects. The proposed model presents a greater computational efficiency compared to full three-dimensional methodologies, without compromising the precision of the results. This allows the implementation of the sound radiation calculation in optimization algorithms with the aim of achieving quieter designs of railway wheels.
27
Lalanne, Bernard, i Maurice Touratier. "Aeroelastic Vibrations and Stability in Cyclic Symmetric Domains". International Journal of Rotating Machinery 6, nr 6 (2000): 445–52. http://dx.doi.org/10.1155/s1023621x00000403.
Pełny tekst źródłaStreszczenie:
This paper deals with rotating cyclic symmetric structures, immersed in light fluid flow. Firstly, general and usual cyclic symmetric properties are recovered from the Floquet theorem for differential equations, having space periodic coefficients in conjunction with a discrete space Fourier series development. The approach for aeroelastic problem having cyclic symmetry is then formulated based on the twin mode approach. In addition to modal one, rotating and stationary wave bases are introduced to derive the equilibrium equations for a non-dissipative system subjected to aerodynamic loading. Rotating wave basis is the natural one, and it also permits consistently to prescribe the aerodynamic pressure on the boundary between the fluid and the structure. The aerodynamic load is then derived from a harmonic analysis of the fluid flow extending to turbomachinery as in the case of aeroplane wing. In this way, aerodynamic forces may be obtained as general as required, depending on successive time derivatives of degrees of freedom in addition to themselves. Finally, some special cases are given and stability is studied for a cyclic periodic blade assembly, even when mistuning between sectors can occur.
28
Al Mahturi, F. S., i D. V. Samokhvalov. "Steel losses analysis in of a BLDC motor using linear approximation of voltage pulses". LETI Transactions on Electrical Engineering & Computer Science 15, nr 5/6 (2022): 80–90. http://dx.doi.org/10.32603/2071-8985-2022-15-5/6-80-90.
Pełny tekst źródłaStreszczenie:
Analysis of iron loss of a BLDC motor is of particular interest at the design stage or when researching methods to improve energy efficiency. Most of the existing methods for determining losses in steel are based on the analysis of losses for individual harmonic components of induction with their subsequent summation. However, the application of these methods for various forms of voltage obtained at the output of the converter is incorrect due to the non-linearity of magnetic circuits. This paper proposes a method for determining steel losses of BLDC motor using a linear approximation of voltage pulses, which makes it possible to take into account the influence of the voltage shape on the magnitude of magnetic induction directly, without expansion into a Fourier series. The dependences of steel losses on the switching frequency for various values of the duty cycle, and on the rise time of voltage pulses are obtained. Comparison of the simulation results of the 5 kW BLDC Motor with the experimental data of the idling mode given by the manufacturer proved the adequacy of the considered method.
29
Bogomolov, Alexander, Victor Nevezhin, Elena Piskun i Vladimir Khokhlov. "Models of Frequency Characteristics of Ecological Systems and their Conversion to Sound Form". E3S Web of Conferences 161 (2020): 01061. http://dx.doi.org/10.1051/e3sconf/202016101061.
Pełny tekst źródłaStreszczenie:
Real-time monitoring of the state of ecological systems can contribute to early warning of their deviation from an equilibrium state (homeostasis) or a change that leads to a threat to human health or existence. In addition to the existing means of monitoring the state of ecological systems and models for predicting the assessment of their state in the future, it is proposed to use models of the frequency characteristics of these systems, monitoring of which can detect signals about the appearance of unwanted deviations from homeostasis in the form of a change in the frequency spectrum. A change in the frequency spectrum can be converted into the sound waveform, which will allow timely detection of this undesirable change in the state of the ecological system. As a new information channel and analysis of the dynamics of the state of ecological systems, in the article it is proposed to use the wavelet transform of time series with the subsequent translation of the totality of their harmonic vibrations into sound form. In contrast to the Fourier transform, in which the spectrum of stationary and non-stationary processes is practically indistinguishable and it is impossible to determine the moment of the appearance of a new harmonic, the wavelet transformation gives this opportunity. In addition to the purely utilitarian application of the conversion of the vibrational characteristics of an ecological system into sound form, it becomes be possible to convert them into the “music” of ecological systems, which may give a new direction for creative understanding of the state of nature.
30
Coffey, M. P., G. Simm i S. Brotherstone. "Energy balance profiles for the first three lactations of dairy cows estimated using random regression". Proceedings of the British Society of Animal Science 2002 (2002): 42. http://dx.doi.org/10.1017/s1752756200006980.
Pełny tekst źródłaStreszczenie:
The replacement of lost body tissue in modern dairy cows usually takes place later in the same lactation, once milk output begins to decline. Individual cows may not regain all lost body energy in the first lactation leading to a greater deficit to be replenished in the second. This results in carry-over effects from one lactation to the next, on both yield and non-yield traits. The use of random regressions and Fourier series allows modelling of cyclical changes in a trait over seasons (Meyer, 2000) and could be used to model multiple lactation energy balance changes in dairy cows. Parameters of these cyclical functions might then be analysed for relationships with traits of economic importance such as health, fertility and survival. The objectives of this study were 1) to model phenotypic daily milk yield, fresh feed intake, liveweight and condition score using random regression techniques, 2) to combine daily estimates obtained in objective 1) into an overall energy balance for each day of the first three successive lactations, 3) to compare energy balance curves over three lactations and 4) to investigate the feasibility of modelling energy balance in the first three lactations using harmonic analysis.
31
Xiong, Yangshou, Kang Huang, Fengwei Xu, Yong Yi, Meng Sang i Hua Zhai. "Research on the Influence of Backlash on Mesh Stiffness and the Nonlinear Dynamics of Spur Gears". Applied Sciences 9, nr 5 (12.03.2019): 1029. http://dx.doi.org/10.3390/app9051029.
Pełny tekst źródłaStreszczenie:
In light of ignoring the effect of backlash on mesh stiffness in existing gear dynamic theory, a precise profile equation was established based on the generating processing principle. An improved potential energy method was proposed to calculate the mesh stiffness. The calculation result showed that when compared with the case of ignoring backlash, the mesh stiffness with backlash had an obvious decrease in a mesh cycle and the rate of decline had a trend of decreasing first and then increasing, so a stiffness coefficient was introduced to observe the effect of backlash. The Fourier series expansion was employed to fit the mesh stiffness rather than time-varying mesh stiffness, and the stiffness coefficient was fitted with the same method. The time-varying mesh stiffness was presented in terms of the piecewise function. The single degree of freedom model was employed, and the fourth order Runge–Kutta method was utilized to investigate the effect of backlash on the nonlinear dynamic characteristics with reference to the time history chart, phase diagram, Poincare map, and Fast Fourier Transformation (FFT) spectrogram. The numerical results revealed that the gear system primarily performs a non-harmonic-single-periodic motion. The partially enlarged views indicate that the system also exhibits small-amplitude and low-frequency motion. For different cases of backlash, the low-frequency motion sometimes shows excellent periodicity and stability and sometimes shows chaos. It is of practical guiding significance to know the mechanisms of some unusual noises as well as the design and manufacture of gear backlash.
32
Yakimov, Vladimir. "Discrete Time Sequence Reconstruction of a Signal Based on Local Approximation Using a Fourier Series by an Orthogonal System of Trigonometric Functions". Informatics and Automation 21, nr 5 (28.09.2022): 1016–43. http://dx.doi.org/10.15622/ia.21.5.7.
Pełny tekst źródłaStreszczenie:
The article considers the development of mathematical and algorithmic support for the sample’s reconstruction in problem sections of a discrete sequence of a continuous signal. The work aimed to ensure the reconstruction of lost samples or sections of samples with a non-constant distorted time grid when sampling a signal with a uniform step and at the same time to reduce the computational complexity of digital reconstruction algorithms. The solution to the stated problem is obtained based on the local approximation method. The specific of this method application was the use of two subsequences of samples located symmetrically concerning the reconstructed section of the sequence. The approximating model is a Fourier series on an orthogonal system of trigonometric functions. The optimal solution to the approximation problem is based on the minimum square error criterion. Mathematical equations are obtained for this type of error. They allow us to estimate its value depending on the model order and the samples number in the subsequences used in the reconstruction process. The peculiarity of the mathematical equations obtained in this paper for signal reconstruction is that they do not require the preliminary calculation of the Fourier series coefficients. They provide a direct calculation of the values of reconstructed samples. At the same time, when the number of samples in the subsequences used for reconstruction will be even, it is not necessary to perform multiplication operations. All this made it possible to reduce the computational complexity of the developed algorithm for signal reconstruction. Experimental studies of the algorithm were carried out based on simulation modeling using a signal model that is an additive sum of harmonic components with a random initial phase. Numerical experiments have shown that the developed algorithm provides the reconstruction result of signal samples with a sufficiently low error. The algorithm is implemented as a software module. The operation of the module is carried out on the basis of asynchronous control of the sampling reconstruction process. It can be used as part of metrologically significant software for digital signal processing systems.
33
Hasheminejad, Seyyed M., i Amir K. Miri. "Effect of Inter-Fibre Distance on Energy Transfer in Unidirectional Composites Containing Ultrasonic Waves". Advanced Composites Letters 15, nr 5 (wrzesień 2006): 096369350601500. http://dx.doi.org/10.1177/096369350601500501.
Pełny tekst źródłaStreszczenie:
Interaction of time harmonic monochromatic anti-plane (SH) waves with a pair of parallel unidirected elastic cylindrical fibres embedded in an unbounded elastic matrix is considered. The classical method of separation of variables along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorems for cylindrical wave functions are employed to obtain a series solution in terms of Fourier coefficients. The presented development is illustrated with numerical examples in which the fibres are insonified at end-on/broadside incidence for a relatively wide range of nondimensional frequencies. Particular attention has been focused on the effects of lateral fibre spacing on energy transfer between the fibres and matrix. The numerical results reveal that, while inter-fibre scattering (interference) has a small influence on the normalized fibre energies for broadside incidence at all frequencies, it has a considerable impact on the energy distribution for end-on incidence (fibres positioned in the eclipse configuration) at intermediate and high frequencies. The proposed model can complement acousto-ultrasonic (AU) techniques in non-destructive evaluation of unidirectional fibre-reinforced composite materials which is generally hampered by the highly dense concentration of the fibres. Limiting case is considered and fair agreement with a well-known solution is established.
34
Kerr, Gilbert, Nehemiah Lopez i Gilberto González-Parra. "Analytical Solutions of Systems of Linear Delay Differential Equations by the Laplace Transform: Featuring Limit Cycles". Mathematical and Computational Applications 29, nr 1 (4.02.2024): 11. http://dx.doi.org/10.3390/mca29010011.
Pełny tekst źródłaStreszczenie:
In this paper we develop an approach for obtaining the solutions to systems of linear retarded and neutral delay differential equations. Our analytical approach is based on the Laplace transform, inverse Laplace transform and the Cauchy residue theorem. The obtained solutions have the form of infinite non-harmonic Fourier series. The main advantage of the proposed approach is the closed-form of the solutions, which are capable of accurately evaluating the solution at any time. Moreover, it allows one to study the asymptotic behavior of the solutions. A remarkable discovery, which to the best of our knowledge has never been presented in the literature, is that there are some particular linear systems of both retarded and neutral delay differential equations for which the solution asymptotically approaches a limit cycle. The well-known method of steps in many cases is unable to obtain the asymptotic behavior of the solution and would most likely fail to detect such cycles. Examples illustrating the Laplace transform method for linear systems of DDEs are presented and discussed. These examples are designed to facilitate a discussion on how the spectral properties of the matrices determine the manner in which one proceeds and how they impact the behavior of the solution. Comparisons with the exact solution provided by the method of steps are presented. Finally, we should mention that the solutions generated by the Laplace transform are, in most instances, extremely accurate even when the truncated series is limited to only a handful of terms and in many cases become more accurate as the independent variable increases.
35
Blasiak, Slawomir. "Influence of Thermoelastic Phenomena on the Energy Conservation in Non-Contacting Face Seals". Energies 13, nr 20 (12.10.2020): 5283. http://dx.doi.org/10.3390/en13205283.
Pełny tekst źródłaStreszczenie:
The purpose of this study was to develop a mathematical model for non-contacting face seals to analyze how their performance is affected by thermoelastic phenomena. The model was used to solve thermal conductivity and thermoelasticity problems. The primary goal was to calculate the values of thermal deformations of the sealing rings in a non-contacting face seal with a flexibly mounted rotor (FMR) for a turbomachine. The model assumes the conversion of mechanical energy into heat in the fluid film. The heat flux generated in the fluid film is transferred first to the sealing rings and then to the fluid surrounding them. Asymmetric distribution of temperature within the sealing rings leads to the occurrence of thermal stresses and, consequently, a change in the geometry of the rings. The model is solved analytically. The distributions of temperature fields for the sealing rings in the cross-sections are calculated using the Fourier-Bessel series as a superficial function of two variables (r,z). The thermoelasticity problems described by the Navier equations are solved by applying the Boussinesq harmonic functions and Goodier’s thermoelastic displacement potential function. The proposed method involves solving various theoretical and practical problems of thermoelasticity in FMR-type non-contacting face seals. The solution of the mathematical model was made use of analytical methods, and the most important obtained results are presented in graphical form, such as the temperature distributions and axial thermal distortions in cross-sections of the rings. The calculated thermal deformations of the sealing rings are used to determine the most important seal performance parameters such as the leakage rate and power loss. The article also presents a multi-criteria analysis of seal rings materials and geometry, which makes it easier to choose the type of materials used for the sliding rings.
36
Jiang, Peihong, Zhigang Chu, Yang Zhao i Yang Yang. "Time-domain sound field reconstruction using a rigid spherical microphone array". Journal of the Acoustical Society of America 155, nr 4 (1.04.2024): 2741–55. http://dx.doi.org/10.1121/10.0025774.
Pełny tekst źródłaStreszczenie:
A time-domain approach for interior spherical near-field acoustic holography is proposed to achieve the low-delay reconstruction of time-domain sound fields using a rigid spherical microphone array. This reconstruction encompasses the incident pressure field, the incident radial particle velocity field, and the total pressure field, which includes scattering. The proposed approach derives time-domain radial propagators through the inverse Fourier transform of their frequency-domain counterparts. These propagators are then applied to the array measurements to obtain the time-domain spherical harmonic coefficients of the interior sound field. Given the fact that the time-domain radial propagators possess finite-time support and exhibit significant high-frequency attenuation characteristics, they can be efficiently implemented using finite impulse response (FIR) filters. The proposed approach processes the signal sample-by-sample through these FIR filters, avoiding a series of issues associated with time-frequency transformations in frequency-domain methods. As a result, the approach offers higher accuracy and lower latency in reconstructing non-stationary sound fields compared to its frequency-domain counterpart and thus holds greater potential for real-time applications. Additionally, owing to the scattering effect of the rigid sphere, the approach avoids the impact of spherical Bessel function nulls and does not require the measurement of particle velocities, which renders the measurements cost effective.
37
Vinogradova, Olga, Anna Krupkina, Kseniya Pierpoint i Denis Kokosinskii. "Cyclic dynamic patterns of Russian macroeconomic indicators found by spectral analysis". Moscow University Economics Bulletin, nr 5 (31.10.2021): 3–28. http://dx.doi.org/10.38050/01300105202151.
Pełny tekst źródłaStreszczenie:
The paper proposes a contemporary interdisciplinary method to identify consistent patterns within cyclical dynamics of GDP and its macroeconomics determinants in the Russian Federation. This method may contribute to better recognition of the stages of economic cycle and of potential early predicators to recessions and crises. We first identify the trend component of Russian GDP and then apply the spectral data analysis to its cyclical component which reveals its multi-frequency, and non-linear vibrations. These vibrations are then further investigated by transforming time series data on GDP and its determinants into a frequency spectrum series via Fourier transform techniques. Wavelength scanning of selected macroeconomic indicators shows the basic economic cycle of real GDP with duration time of approx. 3.13 years. Other procyclical indicators nevertheless discover asynchronous behavior towards GDP due to the relative autonomy of the sectors standing behind these indicators. Their autonomy lies behind differences in reaction forces (shifts) and periods (lags) to both internal and external shocks. We estimate differentials between the dynamics of GDP and its determinants by evaluating phase deviations of their pairwise harmonic components, mutual pairwise phase shifts, and by comparison of their pairwise cross-spectrum. The one of output is the quantification of time lags between GDP and key macroeconomic indicators of individual economic sectors. This result reveals the complexity of GDP dynamics that sends an aliased rather than a unit signal to economic agents. Our decomposition of this signal into signals from key economic sectors and quantification of phase discrepancies between sectoral signals may contribute to findings in early crisis predicators. We also estimate the depth and velocity of shocks penetrations into both economy as a whole and its particular sectors.
38
Singh, S., J. Roy, U. Panda, B. Bhattacharyya, V. Morello, B. W. Stappers, P. S. Ray i M. A. McLaughlin. "The GMRT High Resolution Southern Sky Survey for Pulsars and Transients. III. Searching for Long-period Pulsars". Astrophysical Journal 934, nr 2 (1.08.2022): 138. http://dx.doi.org/10.3847/1538-4357/ac7b91.
Pełny tekst źródłaStreszczenie:
Abstract Searching for periodic non-accelerated signals in the presence of ideal white noise using the fully phase-coherent fast-folding algorithm (FFA) is theoretically established as a more sensitive search method than the fast Fourier transform (FFT) search with incoherent harmonic summing. In this paper, we present a comparison of the performance of an FFA search implementation using RIPTIDE and an FFT search implementation using PRESTO, over a range of signal parameters with white noise and with real telescope noise from the Giant Meterwave Radio Telescope (GMRT) High Resolution Southern Sky (GHRSS) survey with the upgraded GMRT (uGMRT). We find that the FFA search with appropriate de-reddening of the time series performs better than the FFT search with spectral whitening for long-period pulsars under real GHRSS noise conditions. We describe an FFA-search pipeline implemented for the GHRSS survey looking for pulsars over a period of 0.1–100 s and up to a dispersion measure of 500 pc cm−3. We processed GHRSS survey data covering ∼1500 deg2 of the sky with this pipeline. We re-detected 43 known pulsars with a better signal-to-noise ratio in the FFA search than in the FFT search. We also report the discovery of two new pulsars, including a long-period pulsar with a short duty cycle, using this FFA-search pipeline. A population of long-period pulsars with periods of several seconds or higher could help constrain the pulsar death line.
39
Vyngra, Alexei Viktorovich. "Developing algorithms and software for power active filters of ship electric power systems". Vestnik of Astrakhan State Technical University. Series: Marine engineering and technologies 2022, nr 2 (31.05.2022): 73–79. http://dx.doi.org/10.24143/2073-1574-2022-2-73-79.
Pełny tekst źródłaStreszczenie:
The use of electrical receivers with a non-linear load on ships significantly affects the electric power characteristics. The main devices that reduce the distortion of the sinusoid of current and voltage in electrical networks are active, passive and combined filters. There are considered the main types and principles of active filters operation, shown the current methods for detecting a distortion and forming a compensating effect by active filters. Using the active filters for electric drives of reciprocating mechanisms with an uneven, but periodic predictable load on the shaft is demonstrated. The operation of such devices in the ship electrical power system worsens the electric power characteristics (e.g. high iTHD, harmonic components). The effectiveness of using an active filter operating on a perturbation from a reference signal for electric drives of reciprocating compressors has been theoretically grounded. There has been presented an algorithm for operation on a perturbation determining the spectrum of the selected interharmonic distortion and presenting it in the form of a Fourier series to create a compensating effect. Application of the algorithm helps increase the speed of the control system, eliminates temporary errors and simplifies the operation of the system. The range of active filters operation according to this algorithm is found limited due to a necessary periodic load or fixed interference. The control software for a three-phase active filter was designed by using the algorithms. The software project is presented in the MATLAB/Simulink mathematical modeling environment. A specific feature of the software using a memory block to organize the calculation of the compensation pattern for harmonic distortion and using the algorithms for generating a compensating signal in the frequency domain. The hardware modeling is considered and the firmware of the board is made. The interface, code and results of the software work are given. It has been inferred that the software effectively controls the power elements of the active filter with current feedback.
40
Uyulan, Caglar, Türker Tekin Ergüzel i Nevzat Tarhan. "Entropy-based feature extraction technique in conjunction with wavelet packet transform for multi-mental task classification". Biomedical Engineering / Biomedizinische Technik 64, nr 5 (25.09.2019): 529–42. http://dx.doi.org/10.1515/bmt-2018-0105.
Pełny tekst źródłaStreszczenie:
Abstract Event-related mental task information collected from electroencephalography (EEG) signals, which are functionally related to different brain areas, possesses complex and non-stationary signal features. It is essential to be able to classify mental task information through the use in brain-computer interface (BCI) applications. This paper proposes a wavelet packet transform (WPT) technique merged with a specific entropy biomarker as a feature extraction tool to classify six mental tasks. First, the data were collected from a healthy control group and the multi-signal information comprised six mental tasks which were decomposed into a number of subspaces spread over a wide frequency spectrum by projecting six different wavelet basis functions. Later, the decomposed subspaces were subjected to three entropy-type statistical measure functions to extract the feature vectors for each mental task to be fed into a backpropagation time-recurrent neural network (BPTT-RNN) model. Cross-validated classification results demonstrated that the model could classify with 85% accuracy through a discrete Meyer basis function coupled with a Renyi entropy biomarker. The classifier model was finally tested in the Simulink platform to demonstrate the Fourier series representation of periodic signals by tracking the harmonic pattern. In order to boost the model performance, ant colony optimization (ACO)-based feature selection method was employed. The overall accuracy increased to 88.98%. The results underlined that the WPT combined with an entropy uncertainty measure methodology is both effective and versatile to discriminate the features of the signal localized in a time-frequency domain.
41
Zarif'yan, Aleksandr, i Andrey Evstaf'ev. "Energy Consumption Quality Indicators in Collector and Asynchronous Traction Drives of AC Electric Locomotives". Proceedings of Petersburg Transport University 20, nr 4 (17.12.2023): 987–98. http://dx.doi.org/10.20295/1815-588x-2023-4-987-998.
Pełny tekst źródłaStreszczenie:
Purpose: To conduct an experimental study of the indicators of electrical energy consumption quality for serially produced freight electric locomotives of alternating current 2(3)ES5K with a collector traction drive and electric locomotives 2(3)ES5S with an asynchronous traction drive, to provide their comparison and comparative analysis. Methods: The main technical characteristics of the collector traction electric drive (TED) NB-514E and asynchronous TED DTA-1100 are presented. A measurement scheme for voltage and current on the power winding of the transformer is proposed. The monitoring of parameters has been carried out directly on electric locomotives using specialized metrological equipment. The processing of experimental data is based on decomposing the original signal into harmonic components using Fast Fourier Transform (FFT). Results: Parameters of voltage and current harmonics, phase shifts, as well as the values of active and reactive power of the corresponding harmonics have been obtained. An analysis of the spectral composition of voltage and current has been performed. Comparative analysis of the results obtained for electric locomotives with collector and asynchronous traction drives in traction mode has shown that the power factor is 0.65 and 0.99, respectively; and the coefficient of non-linear current distortions is 0.53 and 0.15. A conclusion has been drawn regarding significantly higher quality of electrical energy consumption in the asynchronous traction drive. Practical significance: Based on the specific values of the indicators of electrical energy consumption quality in collector and asynchronous traction drives in traction mode, it is possible to proceed to obtaining economic assessments for the transition of the locomotive fleet of Russian Railways (JSCo “RZD”) to nextgeneration electric locomotives of the 2(3)ES5S series.
42
Bialobrzheskyi, O. V., i D. Y. Rod`kin. "Distorting Electrical Power of the Alternating Current in the Simplest Circuit with a Diode". ENERGETIKA. Proceedings of CIS higher education institutions and power engineering associations 62, nr 5 (4.10.2019): 433–44. http://dx.doi.org/10.21122/1029-7448-2019-62-5-433-444.
Pełny tekst źródłaStreszczenie:
The development of electric power industry is accompanied by an increase in the number of consumers subjected to loads with nonlinear characteristics. The arising problem of the distortion of electrical energy that takes place when the mentioned consumers are in operation is partially solved by using means of improving the quality of electrical energy. The increase in the share of small generating plants that are placed in the nodes of consumers exacerbates the interaction of non-linear loads, forming additional parallel streams of electrical energy. Distorted electrical power is not an indication to account. Existing views on distorting power are amenable to criticism. In the well-known works, the proposals for the assessment of power using the quadratic norm and the quadratic norms of its components have been grounded. For the analysis of processes of formation the components of electrical power, a diagram of the simplest circuit containing a series-connected source of electromotive force, resistors and a diode is considered; also, the circuit was conditionally separated into a source and a consumer. The analysis of the power formation of each circuit element is performed with the use of the expression of current and voltage, as periodic functions represented by the trigonometric form of Fourier series. The power components are separated with the use of the known interaction of harmonic components of current and voltage of different orders. For the circuit elements, the power components formed by current and voltage harmonics of the same order are selected as well as power components formed by current and voltage harmonics of different orders, in which, in their turn, the power components are selected that have the same order as the first ones. The power formed by the action of the latter group is proposed to be attributed to the distorting power and to account its action by the corresponding quadratic norm. A numerical calculation has been performed with a use of the specified power component distribution. Time diagrams illustrate the process of interaction of the power components, which–in the case of the diode–leads to no change in power over time.
43
Grabova, Ulyana, i Svetlana Salnikova. "GENERALIZED POISSON INTEGRAL AND ITS APPLIED ASPECTS". Journal of Automation and Information sciences 2 (1.03.2021): 102–11. http://dx.doi.org/10.34229/1028-0979-2021-2-9.
Pełny tekst źródłaStreszczenie:
Mathematical methods based on statistics have been used in sociology for a long time. The functioning of socio-economic and socio-politic systems is a complex process, which is caused by a number of various factors. Thus, the construction of models of socio-economic and socio-politic processes requires solving problems of both the decomposition of structures and processes, and their integration into a single system model, taking into account the changing conditions of the external environment. Mathematical modeling of such problems can be carried out by methods of network analysis or game theory, which allows finding optimal strategies for the behavior of competitive parties. Asymptotic formulations have a central role in game theory, since, due to the complex strategic nature, explicit solutions can be found only in very rare cases. A large number of models created to study complex social processes that occur in society are dynamical systems, or non-autonomous differential equations, or difference equations with a large number of parameters in any cases. In this situation, it is important to choose an appropriate tool for studying the behavior of such systems. In this paper, generalized Poisson delta operators are considered as approximating aggregates, since periodic processes, which are subdivided into harmonic and polyharmonic, provide the internal integrity of complex systems and their dynamic functioning. Questions of the asymptotic behavior of the exact upper bounds for approximations by generalized Poisson delta operators on classes of periodic functions that satisfy the Lipschitz condition are also studied. The received formulas provide a solution to the Kolmogorov-Nikol’ski problem for generalized Poisson delta operators and Lipschitz classes. The proof is based on the use of formulas that give integral representations of the deviations of linear methods generated by linear processes of summation of Fourier series on sets of periodic functions in the uniform metric obtained in the works of L.I. Bausov. The results can be an effective tool for modeling the processes of social dynamics.
44
Williams, Dennis K., i Trevor G. Seipp. "Considerations in the Design and Analysis of an ASME Section VIII, Div. 2 Reactor Support Skirt". Journal of Pressure Vessel Technology 129, nr 2 (19.02.2007): 316–22. http://dx.doi.org/10.1115/1.2722301.
Pełny tekst źródłaStreszczenie:
This paper describes the considerations employed in the finite element analysis of a relatively “short” support skirt on a hydrocarbon reactor vessel. The analysis is accomplished in accordance with ASME B&PV Code, Section VIII, Division 2 alternate rules in conjunction with the guidelines outlined in WRC Bulletin 429. This provides a sound basis for the classification of the calculated stress intensities. The support skirt is capable of sustaining the deadweight load in addition to resisting the effects of thermal displacements, wind loadings, overturning moments from external piping loads on the attached hydrocarbon reactor vessel, and friction between the skirt base plate and concrete foundation. The displacement and thermal boundary conditions are well defined and discussed in detail. The effects of multiple scenarios for the displacement boundary conditions are examined. The skirt design also employs a hot-box arrangement whereby the primary mode of heat transfer is by radiation. A discussion of the two-part analysis is included and details the interaction between the heat transfer analysis and the subsequent structural analysis. The heat transfer finite element analysis is utilized to determine the temperatures throughout the bottom of the vessel shell and head, as well as the integrally attached support skirt. Of prime importance during the analysis is the axial thermal gradient present in the skirt from the base plate up to and slightly beyond the skirt-to-shell junction. While the geometry of the subject vessel and skirt is best described as axisymmetric, the imposed loadings are a mixture of axisymmetric and non-axisymmetric. This combination lends itself to the judicious selection and utilization of the harmonic finite element and properly chosen Fourier series representation of the applied loads. Comparison of the thermally induced axial stress gradient results from the FEA to those obtained by the closed form beam-on-elastic-foundation are also tendered and discussed. Finally, recommendations are included for the design and analysis of critical support skirts for large, heavy-wall vessels.
45
Geeroms, M., M. Marijns, M. Loccufier i D. Aeyels. "Design of a non-linear vibration absorber". International Journal Sustainable Construction & Design 3, nr 2 (6.11.2012): 111–15. http://dx.doi.org/10.21825/scad.v3i2.20563.
Pełny tekst źródłaStreszczenie:
Linear vibration absorbers can only capture certain discrete frequencies. Therefore the useof nonlinear vibration absorbers which can capture a whole range of frequencies is investigated asan alternative. Such a nonlinear vibration absorber has some special characteristics. For examplethere is a certain frequency-energy dependence. To investigate nonlinear dynamical systems thereis a need for new methods. The harmonic balance method is such a method and is discussed. Theidea is to substitute a Fourier series expansion of the solution variables into the system equations and’balance’ them. Furthermore two realisations of a nonlinear energy sink as an example of a nonlinearvibration absorber are discussed. One based on the restoring force in a wire, the other one by forcinga linear spring to follow a certain path. As will be discussed, an analog principle can be used for therealisation of a Duffing type of nonlinear absorber.
46
Jaming, Philippe, Karim Kellay i Chadi Saba. "The Littlewood problem and non-harmonic Fourier series". Mathematische Annalen, 7.08.2023. http://dx.doi.org/10.1007/s00208-023-02692-w.
Pełny tekst źródła
47
Ju, Ren, Wei Fan i Weidong Zhu. "An Efficient Galerkin Averaging-Incremental Harmonic Balance Method Based on the Fast Fourier Transform and Tensor Contraction". Journal of Vibration and Acoustics 142, nr 6 (11.06.2020). http://dx.doi.org/10.1115/1.4047235.
Pełny tekst źródłaStreszczenie:
Abstract An efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method is developed based on the fast Fourier transform (FFT) and tensor contraction to increase efficiency and robustness of the IHB method when calculating periodic responses of complex nonlinear systems with non-polynomial nonlinearities. As a semi-analytical method, derivation of formulae and programming are significantly simplified in the EGA-IHB method. The residual vector and Jacobian matrix corresponding to nonlinear terms in the EGA-IHB method are expressed using truncated Fourier series. After calculating Fourier coefficient vectors using the FFT, tensor contraction is used to calculate the Jacobian matrix, which can significantly improve numerical efficiency. Since inaccurate results may be obtained from discrete Fourier transform-based methods when aliasing occurs, the minimal non-aliasing sampling rate is determined for the EGA-IHB method. Performances of the EGA-IHB method are analyzed using several benchmark examples; its accuracy, efficiency, convergence, and robustness are analyzed and compared with several widely used semi-analytical methods. The EGA-IHB method has high efficiency and good robustness for both polynomial and non-polynomial nonlinearities, and it has considerable advantages over the other methods.
48
Fitzpatrick, Anna, Molly Folino i Andrea Arnold. "Fourier series-based approximation of time-varying parameters in ordinary differential equations". Inverse Problems, 18.01.2024. http://dx.doi.org/10.1088/1361-6420/ad1fe5.
Pełny tekst źródłaStreszczenie:
Abstract Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some unobservable system parameters may vary with time without known evolution models. In this work, we propose a novel approximation method inspired by the Fourier series to estimate time-varying parameters in deterministic dynamical systems modeled with ordinary differential equations. Using ensemble Kalman filtering in conjunction with Fourier series-based approximation models, we detail two possible implementation schemes for sequentially updating the time-varying parameter estimates given noisy observations of the system states. We demonstrate the capabilities of the proposed approach in estimating periodic parameters, both when the period is known and unknown, as well as non-periodic time-varying parameters of different forms with several computed examples using a forced harmonic oscillator. Results emphasize the importance of the frequencies and number of approximation model terms on the time-varying parameter estimates and corresponding dynamical system predictions.
49
Mohammadian, Mostafa, i G. M. Ismail. "Improved harmonic balance method for analyzing asymmetric restoring force functions in nonlinear vibration of mechanical systems". Physica Scripta, 17.06.2024. http://dx.doi.org/10.1088/1402-4896/ad593f.
Pełny tekst źródłaStreszczenie:
Abstract The non-linear differential equation governing some mechanical systems, such as the non-linear vibrations of FG beams resting on a nonlinear foundation, behaves similarly to the oscillations of a non-linear oscillator with an asymmetric restoring force function that includes both odd and non-odd non-linear terms. The objective of this research is to obtain higher-order approximate analytical solutions for such problems by introducing an enhanced harmonic balance method. By building upon the original problem, two new symmetric systems with odd non-linear terms are introduced, and their higher-order approximate analytical solutions are derived using a novel approach. In proposed method, the restoring force function is represented by its Fourier series expansion. Unlike previous papers, linearizing the equation or taking the first derivative of the Fourier series in the subsequent iteration is unnecessary. However, to enhance the solution’s accuracy, the remaining error from each iteration is utilized in the next one. Finally, by combining the results from the two introduced systems, the analytical period and corresponding periodic solution of the original problem can be obtained. This method is applied to the governing differential equation of FG beams resting on non-linear foundations, a physical non-natural oscillator, and conservative Toda oscillator. The key advantages of this approach are its simplicity and its ability to provide highly precise solutions for both small and large amplitudes in a single iteration.
50
Lai, S. K., X. Yang i F. B. Gao. "Analysis of Large-Amplitude Oscillations in Triple-Well Non-Natural Systems". Journal of Computational and Nonlinear Dynamics 14, nr 9 (15.07.2019). http://dx.doi.org/10.1115/1.4043833.
Pełny tekst źródłaStreszczenie:
In this paper, the large-amplitude oscillation of a triple-well non-natural system, covering both qualitative and quantitative analysis, is investigated. The nonlinear system is governed by a quadratic velocity term and an odd-parity restoring force having cubic and quintic nonlinearities. Many mathematical models in mechanical and structural engineering applications can give rise to this nonlinear problem. In terms of qualitative analysis, the equilibrium points and its trajectories due to the change of the governing parameters are studied. It is interesting that there exist heteroclinic and homoclinic orbits under different equilibrium states. By adjusting the parameter values, the dynamic behavior of this conservative system is shifted accordingly. As exact solutions for this problem expressed in terms of an integral form must be solved numerically, an analytical approximation method can be used to construct accurate solutions to the oscillation around the stable equilibrium points of this system. This method is based on the harmonic balance method incorporated with Newton's method, in which a series of linear algebraic equations can be derived to replace coupled and complicated nonlinear algebraic equations. According to this harmonic balance-based approach, only the use of Fourier series expansions of known functions is required. Accurate analytical approximate solutions can be derived using lower order harmonic balance procedures. The proposed analytical method can offer good agreement with the corresponding numerical results for the whole range of oscillation amplitudes.