Bibliographies thématiques / Non-harmonic Fourier series

Littérature scientifique sur le sujet « Non-harmonic Fourier series »

Auteur : Grafiati
Publié le 13 juillet 2024

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Articles de revues sur le sujet "Non-harmonic Fourier series"

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Sedletskii, A. M. « On the summability and convergence of non-harmonic Fourier series ». Izvestiya : Mathematics 64, no 3 (30 juin 2000) : 583–600. http://dx.doi.org/10.1070/im2000v064n03abeh000292.

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NIKOLAEV, NIKOLAY Y., et HITOSHI IBA. « GENETIC PROGRAMMING OF POLYNOMIAL HARMONIC NETWORKS USING THE DISCRETE FOURIER TRANSFORM ». International Journal of Neural Systems 12, no 05 (octobre 2002) : 399–410. http://dx.doi.org/10.1142/s0129065702001242.

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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.
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BRINGMANN, KATHRIN, et OLAV K. RICHTER. « EXACT FORMULAS FOR COEFFICIENTS OF JACOBI FORMS ». International Journal of Number Theory 07, no 03 (mai 2011) : 825–33. http://dx.doi.org/10.1142/s1793042111004617.

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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.
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Strizhkov, I. G., E. N. Chesnyuk et R. B. Goldman. « Harmonic Analysis of Non-sinusoidal Currents During Heating of Transformers ». Machinery and Equipment for Rural Area, no 8 (27 août 2023) : 40–42. http://dx.doi.org/10.33267/2072-9642-2023-8-40-42.

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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.
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Nigmatullin, Raoul R., Airat A. Khamzin et Yangquan Chen. « Approximation of Aperiodic Signals Using Non-Integer Harmonic Series : The Generalized NAFASS Approach ». Fractal and Fractional 7, no 7 (23 juin 2023) : 498. http://dx.doi.org/10.3390/fractalfract7070498.

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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.
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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, no 4 (15 décembre 2021) : 99–115. http://dx.doi.org/10.14498/tech.2021.4.8.

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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.
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Leblanc, Jean L., et Christophe de la Chapelle. « Characterizing Gum Elastomers by Fourier Transform Rheometry ». Rubber Chemistry and Technology 76, no 4 (1 septembre 2003) : 979–1000. http://dx.doi.org/10.5254/1.3547786.

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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.
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Qi, Hui, Gen Chang Zhang et Jing Fu Nan. « Ground Motion of Non-Circular Alluvial Valley for Incident Plane SH-Wave ». Applied Mechanics and Materials 105-107 (septembre 2011) : 2092–97. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.2092.

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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.
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Lindberg, Anders, Bo Lövgren, Jennie Asp, Jérôme Antoni et 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, no 3 (mars 2022) : 1932–43. http://dx.doi.org/10.1121/10.0009847.

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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.
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Sinou, Jean Jacques. « Analysis of the Response of a Rotor System Containing a Breathing Crack ». Key Engineering Materials 413-414 (juin 2009) : 479–86. http://dx.doi.org/10.4028/www.scientific.net/kem.413-414.479.

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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.
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Thèses sur le sujet "Non-harmonic Fourier series"

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Zhong, Hualiang. « Non-harmonic Fourier series and applications ». Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ58195.pdf.

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Alves, Michele de Oliveira. « Um problema de extensão relacionado a raiz quadrada do Laplaciano com condição de fronteira de Neumann ». Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-19012011-231320/.

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Neste trabalho definimos o operador não local, raiz quadrada do Laplaciano com condição de fronteira de Neumann, através do método de extensão harmônica. O estudo foi feito com o auxílio das séries de Fourier em domínios limitados, como sendo o intervalo, o quadrado e a bola. Posteriormente, aplicamos nosso estudo, à problemas elípticos não lineares envolvendo o operador não local raiz quadrada do Laplaciano com condição de fronteira de Neumann.
In this work we define the non-local operator, square root of the Laplacian with Neumann boundary condition, using the method of harmonic extension. The study was done with the aid of Fourier series in bounded domains, as the interval, the square and the ball. Subsequently, we apply our study, the nonlinear elliptic problems involving non-local operator square root of the Laplacian with Neumann boundary condition.
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Wang, Simeng. « Some problems in harmonic analysis on quantum groups ». Thesis, Besançon, 2016. http://www.theses.fr/2016BESA2062/document.

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Cette thèse étudie quelques problèmes d’analyse harmonique sur les groupes quantiques compacts. Elle consiste en trois parties. La première partie présente la théorie Lp élémentaire des transformées de Fourier, les convolutions et les multiplicateurs sur les groupes quantiques compacts, y compris la théorie de Hausdorff-Young et les inégalités de Young.Dans la seconde partie, nous caractérisons les opérateurs de convolution positifs sur un groupe quantique fini qui envoient Lp dans L2, et donnons aussi quelques constructions sur les groupes quantiques compacts infinis. La méthode pour étudier les états non-dégénérés fournit une formule générale pour calculer les états idempotents associés aux images deHopf, qui généralise un travail de Banica, Franz et Skalski. La troisième partie est consacrée à l’étude des ensembles de Sidon, des ensembles _(p) et des notions associées pour les groupes quantiques compacts. Nous établissons différentes caractérisations des ensembles de Sidon, et en particulier nous démontrons que tout ensemble de Sidon est un ensemble de Sidon fort au sens de Picardello. Nous donnons quelques liens entre les ensembles de Sidon, les ensembles _(p) et les lacunarités pour les multiplicateurs de Fourier sur Lp, généralisant un travail de Blendek et Michali˘cek. Nous démontrons aussi l’existence des ensembles de type _(p) pour les systèmes orthogonaux dans les espaces Lp non commutatifs, et déduisons les propriétés correspondantes pour les groupes quantiques compacts. Nous considérons aussi les ensembles de Sidon centraux, et nous prouvons que les groupes quantiques compacts ayant les mêmes règles de fusion et les mêmes fonctions de dimension ont des ensemble de Sidon centraux identiques. Quelques exemples sont aussi étudiés dans cette thèse. Les travaux présentés dans cette thèse se basent sur deux articles de l’auteur. Le premier s’intitule “Lp-improving convolution operators on finite quantum groups” et a été accepté pour publication dans Indiana University Mathematics Journal, et le deuxième est un travail intitulé “Lacunary Fourier series for compact quantum groups” et a été publié en ligne dans Communications in Mathematical Physics
This thesis studies some problems in the theory of harmonic analysis on compact quantum groups. It consists of three parts. The first part presents some elementary Lp theory of Fourier transforms, convolutions and multipliers on compact quantum groups, including the Hausdorff-Young theory and Young’s inequalities. In the second part, we characterize positive convolution operators on a finite quantum group G which are Lp-improving, and also give some constructions on infinite compact quantum groups. The methods for ondegeneratestates yield a general formula for computing idempotent states associated to Hopf images, which generalizes earlier work of Banica, Franz and Skalski. The third part is devoted to the study of Sidon sets, _(p)-sets and some related notions for compact quantum groups. We establish several different characterizations of Sidon sets, and in particular prove that any Sidon set in a discrete group is a strong Sidon set in the sense of Picardello. We give several relations between Sidon sets, _(p)-sets and lacunarities for Lp-Fourier multipliers, generalizing a previous work by Blendek and Michali˘cek. We also prove the existence of _(p)-sets for orthogonal systems in noncommutative Lp-spaces, and deduce the corresponding properties for compact quantum groups. Central Sidon sets are also discussed, and it turns out that the compact quantum groups with the same fusion rules and the same dimension functions have identical central Sidon sets. Several examples are also included. The thesis is principally based on two works by the author, entitled “Lp-improvingconvolution operators on finite quantum groups” and “Lacunary Fourier series for compact quantum groups”, which have been accepted for publication in Indiana University Mathematics Journal and Communications in Mathematical Physics respectively
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Livres sur le sujet "Non-harmonic Fourier series"

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Young, Robert M. Introduction to Non-Harmonic Fourier Series, Revised Edition, 93. Elsevier Science & Technology Books, 2001.

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Chapitres de livres sur le sujet "Non-harmonic Fourier series"

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Levinson, Norman. « On Non-Harmonic Fourier Series ». Dans Selected Papers of Norman Levinson, 66–83. Boston, MA : Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-5335-8_6.

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« Non-harmonic Fourier Series and Exact Observability ». Dans Observation and Control for Operator Semigroups, 261–85. Basel : Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8994-9_8.

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« Non-harmonic Fourier series (behaviour on the initial interval) ». Dans Fourier Transforms and Approximations, 131–58. CRC Press, 2000. http://dx.doi.org/10.1201/9781482296938-11.

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« Non-harmonic Fourier series (behaviour on the real line) ». Dans Fourier Transforms and Approximations, 159–88. CRC Press, 2000. http://dx.doi.org/10.1201/9781482296938-12.

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Actes de conférences sur le sujet "Non-harmonic Fourier series"

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Jaming, Philippe, Karim Kellay et Chadi Saba. « The Littlewood problem and non-harmonic Fourier series ». Dans 2023 International Conference on Sampling Theory and Applications (SampTA). IEEE, 2023. http://dx.doi.org/10.1109/sampta59647.2023.10301378.

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Haque, Imtiaz, et Juergen Schuller. « Fourier Series-Based Neural Networks for Vehicle System Identification ». Dans ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0331.

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Abstract The use of neural networks in system identification is an emerging field. Neural networks have become popular in recent years as a means to identify linear and non-linear systems whose characteristics are unknown. The success of sigmoidal networks in parameter identification has been limited. However, harmonic activation-based neural networks, recent arrivals in the field of neural networks, have shown excellent promise in linear and non-linear system parameter identification. They have been shown to have excellent generalization capability, computational parallelism, absence of local minima, and good convergence properties. They can be used in the time and frequency domain. This paper presents the application of a special class of such networks, namely Fourier Series neural networks (FSNN) to vehicle system identification. In this paper, the applications of the FSNNs are limited to the frequency domain. Two examples are presented. The results of the identification are based on simulation data. The first example demonstrates the transfer function identification of a two-degree-of freedom lateral dynamics model of an automobile. The second example involves transfer function identification for a quarter car model. The network set-up for such identification is described. The results of the network identification are compared with theory. The results indicate excellent prediction properties of such networks.
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Tian, Jiale, Baisong Yang, Lie Yu et Jian Zhou. « An Investigation on the Static Performance of the Non-Circular Journal Bearing Using Fourier Analysis ». Dans ASME Turbo Expo 2018 : Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-77210.

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As one of the most important components in a rotor-bearing system, journal bearings provide proper support and damping to the rotor so that it can run both smoothly and efficiently and keep stable under different working conditions. As the rotating speed of the rotor growing faster and load getting heavier, the traditional cylinder journal bearing can no longer meet the demand of stabilizing the rotor, so different kinds of non-circular journal bearings were invented, such as elliptical bearing, multi-lobe bearing, wave bearing and etc., to provide better stability and greater load capacity. However, these kinds of non-circular bearings were mostly designed by experience of the engineers, and also the current hydrodynamic bearing design methodology still depends on empirical design. There lacks of corresponding theoretical foundation. In order to develop a theoretical method for bearing designing, an innovative analyzing approach needs to be carried out to explore the mechanism of the bearings and its performance. In this paper, a new approach is presented focusing on the profile of each bearing and their film thickness. A universal mathematical expression for different types of non-circular bearings has been put forward based on the Fourier series theory. The influence of periodic harmonics of film thickness on the static performance of non-circular bearings of finite length is studied for incompressible lubricant. The results show that the film thickness can always be expanded into a Fourier series, and the harmonic components of film pressure can be obtained by solving the Reynolds equation. Finally, the relation between the k-th order harmonic component H0,k and the corresponding static pressure component P0,k is established. This new investigation can be used to improve the non-circular bearing designing methodology with theoretical guidance.
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Jaumouille´, Vincent, et Jean-Jacques Sinou. « Dynamic Analysis of Structures With Nonlinear Bolted Joints by Using an Adaptive Harmonic Balance Method ». Dans ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87162.

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Aeronautical structures are commonly assembled with bolted joints in which friction phenomena provide damping on the dynamic behaviour. Some models, mostly non linear, have consequently been developed and the harmonic balance method (HBM) is adapted to compute non linear response functions in the frequency domain. The basic idea is to develop the response as a Fourier series and to solve equations linking Fourier coefficients. One specific HBM feature is that response accuracy improves as the number of harmonics increases, at the expense of larger computational time. Thus the aim of this study is to develop an adaptive HBM which appreciates numerically the contribution of each harmonic on the dynamic response. For a given precision, the number of retained harmonics is adapted by an algorithm which integrates a numerical criterion based on an approximate strain energy. The application case is an asymmetrical two cantilever beam system linked by a bolted joint represented by a nonlinear LuGre model. Condensation and continuation methods are used to accelerate calculation. Adaptive HBM shows that, for a given value of the criterion, the number of harmonics may increase on resonances indicating that non linear effects are predominant.
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Ju, R., W. Fan et W. D. Zhu. « An Efficient Galerkin Averaging-Incremental Harmonic Balance Method Based on the Fast Fourier Transform and Tensor Contraction ». Dans ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-24009.

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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 nonpolynomial nonlinearities, and it has considerable advantages over the other methods.
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Thomas, O., A. Lazarus et C. Touze´. « A Harmonic-Based Method for Computing the Stability of Periodic Oscillations of Non-Linear Structural Systems ». Dans ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28407.

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In this paper, we present a validation on a practical example of a harmonic-based numerical method to determine the local stability of periodic solutions of dynamical systems. Based on Floquet theory and Fourier series expansion (Hill method), we propose a simple strategy to sort the relevant physical eigenvalues among the expanded numerical spectrum of the linear periodic system governing the perturbed solution. By mixing the Harmonic Balance Method and Asymptotic Numerical Method continuation technique with the developed Hill method, we obtain a purely-frequency based continuation tool able to compute the stability of the continued periodic solutions in a reduced computation time. This procedure is validated by considering an externally forced string and computing the complete bifurcation diagram with the stability of the periodic solutions. The particular coupled regimes are exhibited and found in excellent agreement with results of the literature, allowing a method validation.
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Wu, Jun, Q. J. Ge, Feng Gao et W. Z. Guo. « On the Extension of a Fourier Descriptor Based Method for Four-Bar Linkage Synthesis for Generation of Open and Closed Paths ». Dans ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29028.

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In an earlier work, we have presented an efficient method for synthesizing crank-rocker mechanisms that are capable of generating perceptually simple and smooth low-harmonic closed curves. In this paper, we seek to extend this approach to the synthesis of four-bar linkages for the generation of open curves. Instead of using Fourier transform that requires a function to be defined over the entire period, we combine finite Fourier series in a curve-fitting scheme for the approximation of periodic as well as non-periodic paths. This yields a general method for four-bar path generation that is applicable to both closed and open paths.
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Rahmati, M. T., L. He et R. G. Wells. « Interface Treatment for Harmonic Solution in Multi-Row Aeromechanic Analysis ». Dans ASME Turbo Expo 2010 : Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-23376.

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In the present work, an interface treatment method has been developed to extend a non-linear harmonic solution method for aeromechanic analysis in multiple blade row configurations. The main emphasis is two folds. Firstly the method will enable efficient and accurate analysis of blade aerodynamic forcing and damping characteristics under the influence of adjacent bladerows. Secondly, it will warrant that the same steady/mean base flow as defined by the aerothermal designers is used consistently in the aeromechanical analysis. For passing the harmonic disturbance across a rotor-stator interface, the present method employs the time series reconstruction in conjunction with a temporal Fourier transform. On the other hand, the consistency with a conventional steady multistage solution for the base flow is achieved by applying an extended mixing plane method. The validity and effectiveness of the method are examined and demonstrated.
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Wang, Jianping, Pengfei Li, Ziying Wu et Minghong Zhang. « Harmonic Resonance Frequency Factor of Spur Gear System and Oscillation Reduction Approaches ». Dans ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43188.

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In this study, a non-linear time-varying dynamic model of a spur gear pair system is used to investigate the dynamic behavior of the system by means of multiple scale approach. Both time-varying stiffness, transmission error and tooth backlash clearance of the system are taken into account in the model. The mesh stiffness fluctuation is developed as high order Fourier series and tooth backlash clearance is fitted by high order polynomial function. The frequency factors of the system are investigated and the frequency-response equations at the case of internal and external excitation, parametric excitation and combined excitation are obtained. The peak value of the amplitude of the primary resonance, super and sub harmonic resonance and combination harmonic under internal, external and parametric excitation are researched. The approaches of vibration reduction are investigated. Finally an example is investigated using the presented process and the results indicate the sensitivity and correctness of the presented analysis approaches.
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Vilmin, S., E. Lorrain, Ch Hirsch et M. Swoboda. « Unsteady Flow Modeling Across the Rotor/Stator Interface Using the Nonlinear Harmonic Method ». Dans ASME Turbo Expo 2006 : Power for Land, Sea, and Air. ASMEDC, 2006. http://dx.doi.org/10.1115/gt2006-90210.

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The paper presents results of the incorporation of the harmonic nonlinear method into an existing turbomachinery Navier-Stokes code. This approach, introduced by He and Ning in 1998, can be considered as a bridge between classical steady state and full unsteady calculations, providing an approximate unsteady solution at affordable calculation costs. The unsteady flow perturbation is Fourier decomposed in time, and by a casting in the frequency domain transport equations are obtained for each time frequency. The user controls the accuracy of the unsteady solution through the order of the Fourier series. Alongside the solving of the time-averaged flow steady-state equations, each frequency requires the solving of two additional sets of conservation equations (for the real and imaginary parts of each harmonic). The method is made nonlinear by the injection of the so-called deterministic stresses, resulting from all the solved frequencies, into the time-averaged flow solver. Because of the transposition to the frequency domain, only one blade channel is required like a steady flow simulation. The presented method also features a new improved treatment that enhances the flow continuity across the rotor/stator interface by a reconstruction of the harmonics and the time-averaged flow on both sides of the interface. A non-reflective treatment is applied as well at each interface. Validation for analytical and turbomachinery test cases are presented. In particular, results are compared between the harmonic method, steady-state mixing plane and full unsteady calculations. The comparison with the reference full unsteady calculation provides a quantitative indication of the accuracy of the approach, as well as the significant gain in CPU time, whereas the comparison with classical quasi-steady state solutions indicates the gain of accuracy. A multistage compressor flow is also presented to show the capabilities of the method.
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