Journal ArticleDOI
Free vibrations of beams with general boundary conditions
TLDR
In this paper, a simple and unified approach for the vibration analysis of a generally supported beam is presented, where the flexural displacement of the beam is sought as the linear combination of a Fourier series and an auxiliary polynomial function.About:Â
This article is published in Journal of Sound and Vibration.The article was published on 2000-11-02. It has received 295 citations till now. The article focuses on the topics: Discrete Fourier series & Fourier series.read more
Citations
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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.
Journal ArticleDOI
An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports
TL;DR: In this paper, the displacement solution is expressed as a two-dimensional Fourier series supplemented with several one-dimensional series, which is capable of representing any function (including the exact displacement solution) whose third-order partial derivatives are (required to be) continuous over the area of the plate.
Journal ArticleDOI
Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions
TL;DR: In this paper, a 3D exact solution for the free vibrations of arbitrarily thick functionally graded rectangular plates with general boundary conditions is presented, where the displacement fields are constructed adequately smooth throughout the entire solution domain, an exact solution is obtained based on Rayleigh-Ritz procedure by the energy functions of the plate.
Journal ArticleDOI
A unified solution for vibration analysis of functionally graded cylindrical, conical shells and annular plates with general boundary conditions
TL;DR: In this paper, a unified solution method for free vibration analysis of functionally graded cylindrical, conical shells and annular plates with general boundary conditions is presented by using the first-order shear deformation theory and Rayleigh-Ritz procedure.
References
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Journal ArticleDOI
Free vibration analysis of circular cylindrical shells
TL;DR: In this paper, a general analytical method is presented for evaluating the free vibration characteristics of a circular cylindrical shell with classical boundary conditions of any type, and the solution is obtained through a direct solution procedure in which Sanders' shell equations are used with the axial modal displacements represented as simple Fourier series expressions.
Journal ArticleDOI
Free vibrations of a beam-mass system with elastically restrained ends
TL;DR: In this paper, a beam with an arbitrarily placed concentrated mass and elastically restrained against rotation at either end is solved by using Laplace transforms, and the effect of neglecting the mass of the beam is considered.
Journal ArticleDOI
Dynamic analysis of generally supported beams using fourier series
J.T.-S. Wang,Chi-Chang Lin +1 more
TL;DR: In this paper, the applicability of Fourier series to the dynamic analysis of beams having arbitrary boundary conditions is explored, and a unified and systematic procedure which is seemingly simpler and more straightforward than the conventional modal analysis is presented.