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 paper, a unified method is presented for the vibration analysis of the plates mentioned above with general boundary conditions based on the first-order shear deformation theory and Ritz procedure.
Abstract: The vibrations of functionally graded circular plates, annular plates, and annular, circular sectorial plates have been traditionally treated as different boundary value problems, which results in numerous specific solution algorithms and procedures. It is the problem itself that has been an overwhelming task for a new researcher or application engineer to comprehend. Furthermore each type of plate usually needs treating separately when different boundary conditions are involved. In this paper, a unified method is presented for the vibration analysis of the plates mentioned above with general boundary conditions based on the first-order shear deformation theory and Ritz procedure. The material properties are assumed to vary continuously through the thickness according to the general four-parameter power-law distribution. Regardless of the shapes of the plates and the types of boundary conditions, the displacements of the plates are described as an improved Fourier series expansion which is composed of a double Fourier cosine series and several auxiliary functions. As an innovative point of this work, the auxiliary functions are introduced to eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries and to accelerate the convergence of series representations. The accuracy, reliability and versatility of the current solution are fully demonstrated and verified through numerical examples involving plates with various shapes and boundary conditions. Some new results of functionally graded circular, annular and sector plates with various boundary conditions are presented, which may serve as datum solutions for future computational methods. In addition, the influence of boundary conditions, the material and geometric parameters on the vibration characteristics of the plates are also reported.
104 citations
TL;DR: In this paper, a new method for the resolution of the Gibbs phenomenon based on Gegenbauer polynomials orthogonal with respect to the weight function (1 - x2)λ-1/2 was proposed.
103 citations
TL;DR: In this paper, Fourier series analysis is used to add new insight to the phenomenon of asymmetrical asymmetric dominant frequencies in epicyclic gear systems, and the results are illustrated on vibration data recorded from a Cobra AH-1S helicopter gearbox.
Abstract: Synchronous averaging is difficult to use with epicyclic gear systems because the dominant frequencies are slightly skewed and asymmetrical. This Tech Brief uses Fourier series analysis to add new insight to this phenomenon. The results are illustrated on vibration data recorded from a Cobra AH-1S helicopter gearbox.
103 citations
TL;DR: The stochastic properties of cosmological perturbations are best defined through the Fourier expansion in a finite box as discussed by the authors, and the reasons for that with reference the curvature perturbation, and explore some issues arising from it.
Abstract: The stochastic properties of cosmological perturbations are best defined through the Fourier expansion in a finite box. I discuss the reasons for that with reference the curvature perturbation, and explore some issues arising from it.
103 citations
TL;DR: In this article, it was shown that the Gribov horizon is contained within a certain ellipsoid whose principal axes lie along Fourier coefficients of the connection A (x ).
103 citations