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In this paper, a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method was used to obtain the natural frequencies of rectangular plates. But the results for lower modes were not as good as those obtained by other methods.About:
This article is published in Journal of Sound and Vibration.The article was published on 1986-07-08. It has received 469 citations till now. The article focuses on the topics: Orthogonal polynomials & Libration.read more
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Vibration of Plates
TL;DR: Vibration of Plates as discussed by the authors provides a comprehensive, self-contained introduction to vibration theory and analysis of two-dimensional plates, including boundary characteristically orthogonal polynomials (BCOPs).
Journal ArticleDOI
A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates
TL;DR: In this article, a hyperbolic shear deformation theory applicable to bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates is presented.
Journal ArticleDOI
Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh–Ritz method
TL;DR: In this paper, the free vibration analysis of functionally graded material (FGM) beams subjected to different sets of boundary conditions is performed based on the classical and first order shear deformation beam theories.
Journal ArticleDOI
Vibration analysis of rectangular plates with general elastic boundary supports
TL;DR: In this paper, the Rayleigh-Ritz method is used to determine the modal characteristics of a rectangular plate with general elastic supports alone its edges, and a general approach for deriving a complete set of admissible functions that can be universally applied to various boundary conditions is developed.
Journal ArticleDOI
Free vibrations of cylindrical shells with arbitrary boundary conditions: A comparison study
Zhaoye Qin,Fulei Chu,Jean Zu +2 more
TL;DR: In this article, the free vibration characteristics of cylindrical shells with arbitrary boundary conditions are investigated, and a unified solution for the three different types of expansion functions is developed using the Rayleigh-Ritz method.
References
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Numerical Analysis
TL;DR: This report contains a description of the typical topics covered in a two-semester sequence in Numerical Analysis, and describes the accuracy, efficiency and robustness of these algorithms.
Book
Vibration of plates
TL;DR: The fundamental equation of classical plate theory can be found in this article, where anisotropic and variable-thickness versions of the classical plates are considered, as well as other considerations.
Journal ArticleDOI
The free vibration of rectangular plates
TL;DR: In this article, the free vibration of rectangular plates is analyzed using the Ritz method with 36 terms containing the products of beam functions, including clamped, simply-supported, and free edge conditions.
Journal ArticleDOI
Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method
TL;DR: In this article, a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method was used to obtain the natural frequencies of rectangular plates. But the results for lower modes were not as good as those obtained by other methods.
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K.M. Liew,K.Y. Lam,S.T. Chow +2 more