Topic
Fourier series
About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.
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TL;DR: In this article, the stability and accuracy of three different Fourier expansion-based differential quadrature techniques are shown for the free vibration study of laminated arbitrarily shaped plates, which are used to solve the partial differential system of equations inside each computational element.
Abstract: Summary
In the present paper, strong form finite elements are employed for the free vibration study of laminated arbitrarily shaped plates. In particular, the stability and accuracy of three different Fourier expansion-based differential quadrature techniques are shown. These techniques are used to solve the partial differential system of equations inside each computational element. The three approaches are called harmonic differential quadrature, Fourier differential quadrature and improved Fourier expansion-based differential quadrature methods. The improved Fourier expansion-based differential quadrature method implements auxiliary functions in order to approximate functional derivatives up to the fourth order, with respect to the Fourier differential quadrature method that has a basis made of sines and cosines. All the present applications are related to literature comparisons and the presentation of new results for further investigation within the same topic. A study of such kind has never been proposed in the literature, and it could be useful as a reference for future investigation in this matter. Copyright © 2016 John Wiley & Sons, Ltd.
67 citations
TL;DR: In this article, the Paley-Wiener theorem is used to derive the cardinal function and the central difference expansions of the Whittaker cardinal function, and a bound is obtained on the difference between the cardinal functions and the function which it interpolates.
Abstract: This paper exposes properties of the Whittaker cardinal function and illustrates the use of this function as a mathematical tool. The cardinal function is derived using the Paley-Wiener theorem. The cardinal function and the central-difference expansions arelinked through their similarities. A bound is obtained on the difference between the cardinal func- tion and the function which it interpolates. Several cardinal functions of a number of special functions are examined. It is shown how the cardinal function provides a link between Fourier series and Fourier transforms, and how the cardinal function may be used to solve integral equations.
67 citations
TL;DR: An overview of analytical techniques for the modeling of linear and planar permanent-magnet motors is given in this paper, where the analytical methods describe the magnetic fields based on magnetic surface charges and Fourier series in 2-D and 3-D.
Abstract: In this paper, an overview of analytical techniques for the modeling of linear and planar permanent-magnet motors is given. These models can be used complementary to finite element analysis for fast evaluations of topologies, but they are indispensable for the design of magnetically levitated planar motors and other coreless multi-degrees of freedom motors, which are applied in (ultra) high-precision applications. The analytical methods describe the magnetic fields based on magnetic surface charges and Fourier series in 2-D and 3-D.
67 citations
TL;DR: Through comparative analyses, it is obvious that the present method has a good stable and rapid convergence property and the results of this paper agree closely with the published literature.
Abstract: A semi analytical approach is employed to analyze free vibration characteristics of uniform and stepped circular cylindrical shells subject to arbitrary boundary conditions. The analytical model is established on the basis of multi-segment partitioning strategy and Flugge thin shell theory. The admissible displacement functions are handled by unified Jacobi polynomials and Fourier series. In order to obtain continuous conditions and satisfy arbitrary boundary conditions, the penalty method about the spring technique is adopted. The solutions about free vibration behavior of circular cylindrical shells were obtained by approach of Rayleigh–Ritz. To confirm the reliability and accuracy of this method, convergence study and numerical verifications for circular cylindrical shells subject to different boundary conditions, Jacobi parameters, spring parameters and maximum degree of permissible displacement function are carried out. Through comparative analyses, it is obvious that the present method has a good stable and rapid convergence property and the results of this paper agree closely with the published literature. In addition, some interesting results about the geometric dimensions are investigated.
67 citations
TL;DR: In this paper, a new theoretical model for the antenna is proposed, based on a half-loop driven through an image plane by a coaxial transmission line, with a transverse electromagnetic mode assumed in the aperture of the coaxial line.
Abstract: The conventional Fourier series analysis for the thin-wire circular transmitting loop, or its image equivalent to the half-loop, uses a delta-function generator for excitation. This method of excitation introduces two problems: it does not correspond to any realizable method of feeding the antenna, so an accurate comparison with measurement is not possible, and it produces a divergent series for the input susceptance. To overcome these problems, a new theoretical model is used for the antenna: a half-loop driven through an image plane by a coaxial transmission line, with a transverse electromagnetic mode assumed in the aperture of the coaxial line. This model is solved in a manner that preserves the simplicity of the original Fourier series analysis. All coefficients are obtained as closed-form expressions. Input admittances calculated from this new theoretical model are in excellent agreement with accurate measurements. >
67 citations