Relevant bibliographies by topics / Harmonic Fourier Series coefficient

Academic literature on the topic 'Harmonic Fourier Series coefficient'

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Published: 11 March 2023

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Journal articles on the topic "Harmonic Fourier Series coefficient"

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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 (December 15, 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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Yu, Jun-Yao. "Relationship between Mean Value and Fourier Coefficients of a Time-Varying Function with Half-Period Rests: Theory and Application." Journal of Vibration and Acoustics 116, no. 1 (January 1, 1994): 26–30. http://dx.doi.org/10.1115/1.2930392.

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The Fourier coefficients are investigated for such a periodic time function whose magnitude keeps constant during the time of every half-period. In this case the relationship between the mean value and the Fourier coefficients is achieved using appropriate mathematical theory. It was applied successfully to the study of torsional harmonic excitations due to gas pressure in a four-cycle IC engine. A formula relating the truncated Fourier coefficient series to MIP has been established with very little error. The series simulation of Fourier coefficients is utilized in the determination and analysis of excitations.
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BRINGMANN, KATHRIN, and OLAV K. RICHTER. "EXACT FORMULAS FOR COEFFICIENTS OF JACOBI FORMS." International Journal of Number Theory 07, no. 03 (May 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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Luo, Albert C. J., and Bo Yu. "Bifurcation Trees of Period-1 Motions to Chaos in a Two-Degree-of-Freedom, Nonlinear Oscillator." International Journal of Bifurcation and Chaos 25, no. 13 (December 15, 2015): 1550179. http://dx.doi.org/10.1142/s0218127415501795.

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In this paper, analytical solutions for period-[Formula: see text] motions in a two-degree-of-freedom (2-DOF) nonlinear oscillator are developed through the finite Fourier series. From the finite Fourier series transformation, the dynamical system of coefficients of the finite Fourier series is developed. From such a dynamical system, the solutions of period-[Formula: see text] motions are obtained and the corresponding stability and bifurcation analyses of period-[Formula: see text] motions are carried out. Analytical bifurcation trees of period-1 motions to chaos are presented. Displacements, velocities and trajectories of periodic motions in the 2-DOF nonlinear oscillator are used to illustrate motion complexity, and harmonic amplitude spectrums give harmonic effects on periodic motions of the 2-DOF nonlinear oscillator.
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Rodríguez-Maldonado, Johnny, Cornelio Posadas-Castillo, and Ernesto Zambrano-Serrano. "Alternative Method to Estimate the Fourier Expansions and Its Rate of Change." Mathematics 10, no. 20 (October 17, 2022): 3832. http://dx.doi.org/10.3390/math10203832.

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This paper presents a methodology to obtain the Fourier coefficients (FCs) and the derivative Fourier coefficients (DFCs) from an input signal. Based on the Taylor series that approximates the input signal into a trigonometric signal model through the Kalman filter, consequently, the signal’s and successive derivatives’ coefficients are obtained with the state prediction and the state matrix inverse. Compared to discrete Fourier transform (DFT), the new class of filters provides noise reduction and sidelobe suppression advantages. Additionally, the proposed Taylor–Kalman–Fourier algorithm (TKFA) achieves a null-flat frequency response around the frequency operation. Moreover, with the proposed TKFA method, the decrement in the inter-harmonic amplitude is more significant than that obtained with the Kalman–Fourier algorithm (KFA), and the neighborhood of the null-flat frequency is expanded. Finally, the approximation of the input signal and its derivative can be performed with a sum of functions related to the estimated coefficients and their respective harmonics.
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Tupas, M., C. Navacchi, F. Roth, B. Bauer-Marschallinger, F. Reuß, and W. Wagner. "COMPUTING GLOBAL HARMONIC PARAMETERS FOR FLOOD MAPPING USING TU WIEN’S SAR DATACUBE SOFTWARE STACK." International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLVIII-4/W1-2022 (August 6, 2022): 495–502. http://dx.doi.org/10.5194/isprs-archives-xlviii-4-w1-2022-495-2022.

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Abstract. TU Wien’s flood mapping algorithm, used for global operations, utilizes harmonic functions to model the seasonal behavior of backscatter to improve flood classification. In earth observation (EO), temporal harmonic models have been used in various scenarios for vegetation and water mapping in the optical and, recently, synthetic aperture radar (SAR) domains. These models condense EO time series stacks to a few Fourier coefficient images that capture seasonal variability, allowing for variable estimation for each day of the year. TU Wien’s harmonic parameters consist of these coefficients plus the regression standard deviation and number of observations. However, generating harmonic models at large scales and high resolution presents significant logistical and technical challenges. Particularly for SAR, which requires special handling due to acquisition geometry considerations, implementation on a datacube infrastructure is necessary for agile filtering in metadata, temporal and spatial dimensions. In this work, we highlight our harmonic parameter dataset and our software stack of loosely coupled Python packages, which were deployed in a high-performance computing environment to generate these parameters globally.
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Mallat, Stéphane, Sixin Zhang, and Gaspar Rochette. "Phase harmonic correlations and convolutional neural networks." Information and Inference: A Journal of the IMA 9, no. 3 (November 5, 2019): 721–47. http://dx.doi.org/10.1093/imaiai/iaz019.

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Abstract A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images, convolutional networks often learn a first layer of filters that are well localized in the frequency domain, with different phases. We show that a rectifier then acts as a filter on the phase of the resulting coefficients. It computes signal descriptors that are local in space, frequency and phase. The nonlinear phase filter becomes a multiplicative operator over phase harmonics computed with a Fourier transform along the phase. We prove that it defines a bi-Lipschitz and invertible representation. The correlations of phase harmonics coefficients characterize coherent structures from their phase dependence across frequencies. For wavelet filters, we show numerically that signals having sparse wavelet coefficients can be recovered from few phase harmonic correlations, which provide a compressive representation.
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Bringmann, Kathrin, Paul Jenkins, and Ben Kane. "Differential operators on polar harmonic Maass forms and elliptic duality." Quarterly Journal of Mathematics 70, no. 4 (July 3, 2019): 1181–207. http://dx.doi.org/10.1093/qmath/haz009.

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Abstract In this paper, we study polar harmonic Maass forms of negative integral weight. Using work of Fay, we construct Poincaré series which span the space of such forms and show that their elliptic coefficients exhibit duality properties which are similar to the properties known for Fourier coefficients of harmonic Maass forms and weakly holomorphic modular forms.
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Hong, Xiaobin, Yuan Liu, Xiaohui Lin, Zongqiang Luo, and Zhenwei He. "Nonlinear Ultrasonic Detection Method for Delamination Damage of Lined Anti-Corrosion Pipes Using PZT Transducers." Applied Sciences 8, no. 11 (November 14, 2018): 2240. http://dx.doi.org/10.3390/app8112240.

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Lined anti-corrosion pipes are widely used in oil and gas, petrochemical, pharmaceutical industries. However, defects, especially delamination, may occur in the production and service of pipes which result in safety accidents. Based on nonlinear ultrasonic theory, this paper studied the delamination detection method using the nonlinear harmonics for lined anti-corrosion pipes. The response characteristics of the anti-corrosion pipe were obtained through a sweep sine response experiment and the preferred excitation frequency was determined. The Wavelet Packet transform and Hilbert–Huang transform is applied for signal process and feature extraction. Then, a series of experiments were carried out and the results were analyzed and discussed. The results showed that a second-order and third-order nonlinear coefficient increased with the delamination damage. The amplitude of second-harmonic is much stronger than the third-order one. The mean squared error of the nonlinear coefficient, which was processed by Wavelet Packet transform and Hilbert–Huang transform, is smaller than wavelet packet transform and Discrete Fourier transform or processed only Hilbert–Huang transform. The higher harmonics can describe the change of delamination damage, which means that the nonlinear ultrasonic detection method could use for damage detection of anti-corrosion pipe. The nonlinear higher-harmonic is sensitive to delamination damage. The nonlinear ultrasonic method has the potential for damage detection for lined anti-corrosion pipes.
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Hu, Zhengmin, Kai Zhou, and Yong Chen. "Sound Radiation Analysis of Functionally Graded Porous Plates with Arbitrary Boundary Conditions and Resting on Elastic Foundation." International Journal of Structural Stability and Dynamics 20, no. 05 (May 2020): 2050068. http://dx.doi.org/10.1142/s0219455420500686.

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In this paper, the sound radiation behaviors of the functionally graded porous (FGP) plate with arbitrary boundary conditions and resting on elastic foundation are studied by means of the modified Fourier series method. It is assumed that a total of three types of porosity distributions are considered in the present study. The material parameters are determined according to the porosity coefficient used to denote the size of pores in the plate. The governing equations of the FGP plate are derived by utilizing the Hamilton’s principle on the basis of the first-order deformation theory (FSDT). Each displacement component of the FGP plate is expanded as the Fourier cosine series combined with auxiliary polynomial functions introduced to enhance the convergence rate of the series expansions. The acoustic response of the FGP plate due to a concentrated harmonic load is calculated by evaluating the Rayleigh integral. Good agreements are attained by comparing the present results with those in available literatures, which show the accuracy and versatility of the developed method in this paper. Finally, the influences of the porosity distribution type, porosity coefficient, boundary condition and elastic foundation on the sound radiation of the FGP plate are analyzed in detail.
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Dissertations / Theses on the topic "Harmonic Fourier Series coefficient"

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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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Каща, М. О., and Р. Марченко. "Forecasting the development of COVID-19 in Ukraine by fourier series." Thesis, Sumy State University, 2021. https://essuir.sumdu.edu.ua/handle/123456789/86979.

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Brooks, Evan B. "Fourier Series Applications in Multitemporal Remote Sensing Analysis using Landsat Data." Diss., Virginia Tech, 2013. http://hdl.handle.net/10919/23276.

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Researchers now have unprecedented access to free Landsat data, enabling detailed monitoring of the Earth's land surface and vegetation.  There are gaps in the data, due in part to cloud cover. The gaps are aperiodic and localized, forcing any detailed multitemporal analysis based on Landsat data to compensate.   Harmonic regression approximates Landsat data for any point in time with minimal training images and reduced storage requirements.  In two study areas in North Carolina, USA, harmonic regression approaches were least as good at simulating missing data as STAR-FM for images from 2001.  Harmonic regression had an R^2"0.9 over three quarters of all pixels. It gave the highest R_Predicted^2 values on two thirds of the pixels.  Applying harmonic regression with the same number of harmonics to consecutive years yielded an improved fit, R^2"0.99 for most pixels.   We next demonstrate a change detection method based on exponentially weighted moving average (EWMA) charts of harmonic residuals. In the process, a data-driven cloud filter is created, enabling use of partially clouded data.  The approach is shown capable of detecting thins and subtle forest degradations in Alabama, USA, considerably finer than the Landsat spatial resolution in an on-the-fly fashion, with new images easily incorporated into the algorithm.  EWMA detection accurately showed the location, timing, and magnitude of 85% of known harvests in the study area, verified by aerial imagery.   We use harmonic regression to improve the precision of dynamic forest parameter estimates, generating a robust time series of vegetation index values.  These values are classified into strata maps in Alabama, USA, depicting regions of similar growth potential.  These maps are applied to Forest Service Forest Inventory and Analysis (FIA) plots, generating post-stratified estimates of static and dynamic forest parameters.  Improvements to efficiency for all parameters were such that a comparable random sample would require at least 20% more sampling units, with the improvement for the growth parameter requiring a 50% increase. These applications demonstrate the utility of harmonic regression for Landsat data.  They suggest further applications in environmental monitoring and improved estimation of landscape parameters, critical to improving large-scale models of ecosystems and climate effects.
Ph. D.
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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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Salahifar, Raydin. "Analysis of Pipeline Systems Under Harmonic Forces." Thesis, Université d'Ottawa / University of Ottawa, 2011. http://hdl.handle.net/10393/19820.

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Starting with tensor calculus and the variational form of the Hamiltonian functional, a generalized theory is formulated for doubly curved thin shells. The formulation avoids geometric approximations commonly adopted in other formulations. The theory is then specialized for cylindrical and toroidal shells as special cases, both of interest in the modeling of straight and elbow segments of pipeline systems. Since the treatment avoids geometric approximations, the cylindrical shell theory is believed to be more accurate than others reported in the literature. By adopting a set of consistent geometric approximations, the present theory is shown to revert to the well known Flugge shell theory. Another set of consistent geometric approximations is shown to lead to the Donnell-Mushtari-Vlasov (DMV) theory. A general closed form solution of the theory is developed for cylinders under general harmonic loads. The solution is then used to formulate a family of exact shape functions which are subsequently used to formulate a super-convergent finite element. The formulation efficiently and accurately captures ovalization, warping, radial expansion, and other shell behavioural modes under general static or harmonic forces either in-phase or out-of-phase. Comparisons with shell solutions available in Abaqus demonstrate the validity of the formulation and the accuracy of its predictions. The generalized thin shell theory is then specialized for toroidal shells. Consistent sets of approximations lead to three simplified theories for toroidal shells. The first set of approximations has lead to a theory comparable to that of Sanders while the second set of approximation has lead to a theory nearly identical to the DMV theory for toroidal shells. A closed form solution is then obtained for the governing equation. Exact shape functions are then developed and subsequently used to formulate a finite element. Comparisons with Abaqus solutions show the validity of the formulation for short elbow segments under a variety of loading conditions. Because of their efficiency, the finite elements developed are particularly suited for the analysis of long pipeline systems.
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Ha, Keunsoo. "Position Estimation in Switched Reluctance Motor Drives Using the First Switching Harmonics of Phase Voltage and Current." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/28296.

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Position estimation using only active phase voltage and current is presented to perform high accuracy position sensorless control of a SRM drive. By extracting the amplitude of the first switching harmonic terms of phase voltage and current for a PWM period through Fourier analysis, flux-linkage and position are estimated without external hardware circuitry such as a modulator and demodulator, resulting in increasing cost, as well as large position estimation error produced when the motional back emf is ignored near zero speed. Hence the proposed position estimation scheme covers the entire speed range including the standstill under various loads and it has high resolution information depending on switching frequency. Fourier series and Fast Fourier transform are employed to decompose the phase voltage and current into its first switching harmonic. A two-phase SRM drive system, consisting of an asymmetrical converter and a conventional closed-loop PI current controller, is utilized to validate the performance of the proposed position estimation scheme in comprehensive operating conditions. The estimated values very closely track the actual values in dynamic simulations and experiments. It is shown that the proposed position estimation scheme using Fourier analysis is sufficiently accurate and works satisfactorily at various operating points. This research also proposes an accurate self-inductance measurement method. In general, when applying circulating currents within the body of a ferromagnetic material under conditions of a time varying magnetic flux, the effects of eddy current losses and resistance changes due to heating decrease the magnetic field strength and thereby the reduced magnetic field decreases the magnetic flux-linkage of SRM. These losses make a challenge to the measurement of magnetic characteristics of SRM. These motives lead to propose a measurement methodology based on 60 Hz sinusoidal excitation using a variable AC power supply, which provides an alternative to time domain integration approaches for self-inductance or flux-linkage measurement as well as eliminates error arising from thermal and eddy currents effects. The validation of the proposed method is verified with the correlation between the measurement and FEA results of flux-linkage. Furthermore, this research proposes the solutions for low cost and high efficiency drive systems, consisting of a split AC converter and a two-phase SRM. Its performance is analyzed and verified with experiments at the rated speed under various loads. It is believed that this drive system combined with the proposed position estimation scheme using Fourier analysis is a strong contender to be a low cost motor drive system with single switch per phase having comparable efficiency and acoustic noise level as an asymmetric drive system.
Ph. D.
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Östberg, Martin. "Modelling tools for quieter vehicles : Waves in poro-and visco-elastic continua." Doctoral thesis, KTH, MWL Strukturakustik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-95205.

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New modelling tools intended to contribute to the development of components for quieter vehicles are developed. The tools are based on continuum models for wave propagation in poro– and visco–elastic media. By using geometric attributes of the studied components, the computational cost may be radically decreased compared to traditional methods. By assigning known analytical functions for one or two of the spatial directions, the spatial dimension of the remaining numerical problem is reduced. This reduction of spatial dimensions is performed in two di↵erent ways. The first one treats wave propagation in infinitely extended homogeneous and hollowed cylindrical rods, or wave guides, consisting of visco–elastic media. The wave solutions obtained are then used to model rubber vibration isolators of finite length by mode–matching the fields to the radial boundary conditions of interest. The second one is a method for modelling rotationally symmetric multilayered structures consisting of poro–elastic, elastic and fluid domains. By using a harmonic expansion for the azimuthal spatial dependence, the original three–dimensional problem is split up into several, much smaller, two– dimensional ones, radically decreasing the computational load. Moreover, using a mixed measurement/modelling approach, the audible frequency range characteristics of a viscous damper from a truck is studied, illustrating the influence of the rubber bushings by which it is attached to surrounding structures. The modelling approaches presented in this thesis are intended as tools aiding the design process of new vehicles, enabling new technology striving for more sustainable vehicle concepts. More specifically, the tools aim to improve the modelling of sound and vibration properties which are often penalised when seeking new, more sustainable vehicle designs.

QC 20120522


Centre for Eco2 Vehicle Design
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Vest, Ambroise. "Stabilisation rapide et observation en plusieurs instants de systèmes oscillants." Phd thesis, Université de Strasbourg, 2013. http://tel.archives-ouvertes.fr/tel-00864407.

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Ce travail est constitué de deux parties indépendantes traitant chacune d'un problème issu de la théorie du contrôle des équations aux dérivées partielles. La première partie est consacrée à l'étude d'un feedback explicite et déjà connu, s'appliquant à des systèmes linéaires, réversibles en temps et éventuellement munis d'un opérateur de contrôle non-borné. On justifie le caractère bien posé du problème en boucle fermée via la théorie des semi-groupes puis on étudie le taux de décroissance des solutions du système régulé. La seconde partie concerne un problème d'observation pour la corde vibrante : on détermine comment choisir des instants d'observation pour que la position de la corde à ces instants permette de retrouver les conditions initiales tout en préservant une certaine régularité. La méthode, qui repose sur des résultats d'approximation diophantienne, est ensuite étendue à d'autres systèmes. En utilisant une méthode de dualité on démontre aussi un résultat de contrôlabilité exacte.
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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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Mayer, Jürgen. "Investigation of the biophysical basis for cell organelle morphology." Master's thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-26600.

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It is known that fission yeast Schizosaccharomyces pombe maintains its nuclear envelope during mitosis and it undergoes an interesting shape change during cell division - from a spherical via an ellipsoidal and a peanut-like to a dumb-bell shape. However, the biomechanical system behind this amazing transformation is still not understood. What we know is, that the shape must change due to forces acting on the membrane surrounding the nucleus and the microtubule based mitotic spindle is thought to play a key role. To estimate the locations and directions of the forces, the shape of the nucleus was recorded by confocal light microscopy. But such data is often inhomogeneously labeled with gaps in the boundary, making classical segmentation impractical. In order to accurately determine the shape we developed a global parametric shape description method, based on a Fourier coordinate expansion. The method implicitly assumes a closed and smooth surface. We will calculate the geometrical properties of the 2-dimensional shape and extend it to 3-dimensional properties, assuming rotational symmetry. Using a mechanical model for the lipid bilayer and the so called Helfrich-Canham free energy we want to calculate the minimum energy shape while respecting system-specific constraints to the surface and the enclosed volume. Comparing it with the observed shape leads to the forces. This provides the needed research tools to study forces based on images.
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Books on the topic "Harmonic Fourier Series coefficient"

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Petrovich, Khavin Viktor, and Nikolʹskiĭ N. K, eds. Commutative harmonic analysis IV: Harmonic analysis in IRn̳. Berlin: Springer-Verlag, 1992.

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Elwood, Byerly William. An elementary treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics, with applications to problems in mathematical physics. Mineola, N.Y: Dover Publications, 2003.

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R, Wade W., and Simon P. 1949-, eds. Walsh series: An introduction to dyadic harmonic analysis. Budapest: Akadémiai Kiadó, 1990.

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Schipp, F. Walsh series: An introduction to dyadic harmonic analysis. Bristol [England]: Adam Hilger, 1990.

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D'Angelo, John P. Hermitian analysis: From Fourier series to Cauchy-Riemann geometry. New York: Birkhauser/Springer, 2013.

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Ward, Brown James, ed. Fourier series and boundary value problems. 4th ed. New York: McGraw-Hill, 1987.

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Algebraic topology. Providence, R.I: American Mathematical Society, 1986.

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1968-, Arvesú Jorge, and Lopez Lagomasino Guillermo 1948-, eds. Recent advances in orthogonal polynomials, special functions, and their applications: 11th International Symposium on Orthogonal Polynomials, Special Functions, and Their Applications, August 29-September 2, 2011, Universidad Carlos III de Madrid, Leganes, Spain. Providence, R.I: American Mathematical Society, 2012.

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Harmonic Maass Forms and Mock Modular Forms: Theory and Applications. American Mathematical Society, 2017.

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Stroud, K. A. Fourier Series and Harmonic Analysis. Hyperion Books, 1986.

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Book chapters on the topic "Harmonic Fourier Series coefficient"

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Helson, Henry. "Fourier Series and Integrals." In Harmonic Analysis, 1–49. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4615-7181-0_1.

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Pereyra, María, and Lesley Ward. "Fourier series: Some motivation." In Harmonic Analysis, 1–20. Providence, Rhode Island: American Mathematical Society, 2012. http://dx.doi.org/10.1090/stml/063/01.

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Deitmar, Anton. "Fourier Series." In A First Course in Harmonic Analysis, 3–20. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-3834-6_1.

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Alimov, Sh A., R. R. Ashurov, and A. K. Pulatov. "Multiple Fourier Series and Fourier Integrals." In Commutative Harmonic Analysis IV, 1–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-06301-9_1.

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Pereyra, María, and Lesley Ward. "Pointwise convergence of Fourier series." In Harmonic Analysis, 55–75. Providence, Rhode Island: American Mathematical Society, 2012. http://dx.doi.org/10.1090/stml/063/03.

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Weltner, Klaus, Sebastian John, Wolfgang J. Weber, Peter Schuster, and Jean Grosjean. "Fourier Series; Harmonic Analysis." In Mathematics for Physicists and Engineers, 493–508. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-54124-7_18.

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Weltner, Klaus, Peter Schuster, Wolfgang J. Weber, and Jean Grosjean. "Fourier Series; Harmonic Analysis." In Mathematics for Physicists and Engineers, 491–505. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00173-4_18.

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Pereyra, María, and Lesley Ward. "Mean-square convergence of Fourier series." In Harmonic Analysis, 107–26. Providence, Rhode Island: American Mathematical Society, 2012. http://dx.doi.org/10.1090/stml/063/05.

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Andersson, Mats. "Harmonic Functions and Fourier Series." In Topics in Complex Analysis, 97–111. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-4042-6_7.

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Levinson, Norman. "On Non-Harmonic Fourier Series." In 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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Conference papers on the topic "Harmonic Fourier Series coefficient"

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Schils, George F., and Donald W. Sweeney. "Rotationally invariant correlation filtering for multiple images." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/oam.1985.the2.

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Numerous problems in optical pattern recognition require the classification of a finite number of images regardless of their orientation angles. A method is presented for designing translationally invariant optical correlation filters that produce a specified response to rotations of each of the input images. The correlation filter is formed as an infinite linear combination of the angular Fourier harmonics of the n input images. Imposing the requirements for the specified rotational response of the filter to each input image leads to a vector-matrix convolution equation that is to be solved for the unknown angular weighting coefficients. Expansion into vector-matrix angular Fourier series and term-by-term solution for the Fourier coefficients gives a number of systems of n equations for n unknowns. The elements of the matrix describing each system of equations are the correlations between the angular harmonics of the input images. Inverting this matrix decorrelates the angular harmonics of the input images and allows an arbitrary response to be obtained. Choosing the special case that the rotational responses consist of only one nonzero Fourier series coefficient gives the generalization of the circular harmonic filter to n images. We call this the multiple circular harmonic filter. The classification of n input images can be achieved by choosing the rotational response amplitude to be a different constant value for each image. As shown by examples, this allows multiple input images to be distinguished while preserving rotational invariance.
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Al-Bedoor, B. O., and A. A. Al-Qaisia. "Analysis of Rotating Blade Forced Vibration Due to Torsional Excitation Using the Method of Harmonic Balance." In ASME 2002 Pressure Vessels and Piping Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/pvp2002-1512.

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This paper presents an analysis of the forced vibration of rotating blade due to torsional excitation. The model analyzed is a multi-modal forced second order ordinary differential equation with multiple harmonically varying coefficients. The method of Harmonic Balance (HB) is employed to find approximate solutions for each of the blade modes in the form of truncated Fourier series. The solutions have shown multi resonance response for the first blade vibration mode. The examination of the determinant of the harmonic balance solution coefficient matrix for stability purposes has shown that the region between the two resonance points is an unstable vibration region. Numerical integration of the equations is conducted at different frequency ratio points and the results are discussed. This solution provides a very critical operation and design guidance for rotating blade with torsional vibration excitation.
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Jaumouille´, Vincent, and Jean-Jacques Sinou. "Dynamic Analysis of Structures With Nonlinear Bolted Joints by Using an Adaptive Harmonic Balance Method." In 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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Luo, Albert C. J., Yeyin Xu, and Zhaobo Chen. "On Periodic Motions in the First-Order Nonlinear Systems." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-66219.

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In this paper, analytical solutions of periodic motions in the first-order nonlinear dynamical system are discussed from the finite Fourier series expression. The first-order nonlinear dynamical system is transformed to the dynamical system of coefficients in the Fourier series. From investigation of such dynamical system of coefficients, the analytical solutions of periodic motions are obtained, and the corresponding stability and bifurcation of periodic motions will be determined. In fact, this method provides a frequency-response analysis of periodic motions in nonlinear dynamical systems, which is alike the Laplace transformation of periodic motions for nonlinear dynamical systems. The harmonic frequency-amplitude curves are obtained for different-order harmonic terms in the Fourier series. Through such frequency-amplitude curves, the nonlinear characteristics of periodic motions in the first-order nonlinear system can be determined. From analytical solutions, the initial conditions are obtained for numerical simulations. From such initial conditions, numerical simulations are completed in comparison of the analytical solutions of periodic motions.
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Ju, R., W. Fan, and W. D. Zhu. "An Efficient Galerkin Averaging-Incremental Harmonic Balance Method Based on the Fast Fourier Transform and Tensor Contraction." In 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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Gu, Weiwei, and Zili Xu. "3D Numerical Friction Contact Model and Its Application to Nonlinear Blade Damping." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-22292.

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A three dimensional numerical friction contact model is proposed to investigate the nonlinear vibration of damped blade. The model describes the discrete friction forces in the time domain. By using Discrete Fourier Transforms, the discrete friction forces can be transformed into a series of harmonic functions which are used to solve the nonlinear vibration of damped blade in the frequency domain. The difference between static friction coefficient and dynamic friction coefficient is considered in the model. To consider microslip effect, an array of spring-slider contact pairs (friction contact model) is distributed on the contact surfaces. Additionally, the effect of area of the contact surface on the vibration of damped blade can be studied by altering the number of the contact pairs. Finally, the nonlinear vibration of a real turbine blade with shrouded friction dampers is solved using the proposed friction contact model, Multi-Harmonic Balance Method and Receptance Method.
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Bakeer, Bakeer, Oleg Shiryayev, and Ammaar Tahir. "Trigonometric Collocation for Computation of Steady State Responses of Cracked Structures." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-86682.

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Development of vibration-based structural health monitoring techniques requires the use of various computational methods to predict dynamic responses of damaged structures. The method described in this work can be used for prediction of steady state harmonic responses for structures with fatigue cracks and may have several advantages over alternative techniques. The method appears to be relatively easy to implement and computationally inexpensive. The steady state response of the system at a given number of time points distributed over one vibration period is represented in terms of Fourier series containing higher frequency harmonics. Equations of motion are formulated in the form that allows for easy computation of Fourier coefficients for all terms in the series. Iterative procedure is used for determining the time of stiffness change in order to capture bilinear dynamic behavior. We present results of initial investigation by applying the method to a model of a cantilever beam with a crack.
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Bakeer, Bakeer, and Oleg Shiryayev. "Trigonometric Collocation for Computation of Steady State Response of a Cracked Beam." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-63500.

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Development of vibration-based structural health monitoring techniques requires the use of various computational methods to predict dynamic responses of damaged structures. The method described in this work can be used for prediction of steady state harmonic responses for structures with fatigue cracks and may have several advantages over alternative techniques. The method appears to be relatively easy to implement and computationally inexpensive. The steady state response of the system at a given number of time points distributed over one vibration period is represented in terms of Fourier series containing higher frequency harmonics. Equations of motion are formulated in the form that allows for easy computation of Fourier coefficients for all terms in the series. Iterative procedure is used for determining the time of stiffness change in order to capture bilinear dynamic behavior. We present results of initial investigation by applying the method to a model of a cantilever beam with a crack.
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Weiss, Jonathan M., Venkataramanan Subramanian, and Kenneth C. Hall. "Simulation of Unsteady Turbomachinery Flows Using an Implicitly Coupled Nonlinear Harmonic Balance Method." In ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/gt2011-46367.

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A nonlinear harmonic balance method for the simulation of turbomachinery flows is presented. The method is based on representing an unsteady, time periodic flow by a Fourier series in time and then solving a set of mathematically steady-state equations to obtain the Fourier coefficients. The steady-state solutions are stored at discrete time levels distributed throughout one period of unsteadiness and are coupled via the physical time derivative and at periodic boundaries. Implicit coupling between time levels is achieved in a computationally efficient manner through approximate factorization of the linear system that results from the discretized equations. Unsteady, rotor-stator interactions are performed to validate the implementation. Results based on the harmonic balance method are compared against those obtained using a full unsteady, time-accurate calculation using moving meshes. The implicitly coupled nonlinear harmonic balance method is shown to produce a solution of reasonable accuracy compared to the full unsteady approach but with significantly less computational cost.
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Woo, Ko-Choong, Albert A. Rodger, Richard D. Neilson, and Marian Wiercigroch. "Application of the Harmonic Balance Method to Ground Moling Machines Operating in Periodic Regimes." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21453.

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Abstract The paper describes current research into mathematical modelling of a novel vibro-impact ground moling system. Experimental and theoretical studies suggest periodic responses are required to achieve the optimal penetrating conditions for the ground moling process, as this results in reduced soil penetration resistance. Therefore, there is a practical need for a robust and efficient methodology to calculate periodic responses for a wide range of operational parameters. Due to the structural complexity of a real vibro-impact moling system, the dynamic response of an idealised impact oscillator has been investigated in the first instance. This paper presents a detailed study of periodic responses of the impact oscillator under harmonic forcing using alternating frequency-time harmonic balance method. Recommendations of how to effectively adapt the alternating frequency-time harmonic balance method for a stiff impacting system are given. The periodic motion is represented algebraically by a truncated Fourier series and the systematic methodology employed allows for convergence. The idea central to this procedure is that the linear oscillator is explicitly solvable analytically, and this allows for the initial set of Fourier coefficients. The clearance value is then adjusted so that contact with the secondary stiffness is slight and the nonlinearity is weak. The solution to this subsequent system is obtainable as the initial guess is close to the required solution.
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