Journal ArticleDOI
Finite element displacement method for large amplitude free flexural vibrations of beams and plates
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TLDR
In this article, a finite element method to determine the nonlinear frequency of beams and plates for large amplitude free vibrations is presented, which is characterized by the basic stiffness, mass, geometrical stiffness and the associated inplane force matrices.About:
This article is published in Computers & Structures.The article was published on 1973-01-01. It has received 138 citations till now. The article focuses on the topics: Direct stiffness method & Finite element method.read more
Citations
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Journal ArticleDOI
Nonlinear vibration of Timoshenko beam due to moving loads including the effects of weight and longitudinal inertia of beam
TL;DR: In this paper, the effects of weight and axial inertia of a beam were taken into account for studying the nonlinear vibration of the Timoshenko beam due to external loads, and the combination of Galerkins method and Runge-Kutta method was employed to obtain the dynamic responses of the beam.
Journal ArticleDOI
A unified Fourier spectral method for nonlinear free vibration analysis of the laminated composite and sandwich beams with arbitrary restrained ends
TL;DR: In this article, the effect of the boundary condition on the vibration properties of the laminated composite and sandwich (LC-S) beams was investigated using a modified Fourier spectral method, which is capable of dealing with arbitrary boundary conditions without need to satisfy them in advance.
Book ChapterDOI
Nonlinear Vibrations of Beams Including Shear Deformations and Rotatory Inertia
TL;DR: In this article, the free large-amplitude oscillation of a beam with whatever boundary conditions are investigated on the basis of a polar continuum model in which a priori ordering assumptions are avoided.
References
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Book
Theory of plates and shells
TL;DR: In this article, the authors describe the bending of long RECTANGULAR PLATES to a cycloidal surface, and the resulting deformation of shels without bending the plates.
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
A new approach to the analysis of large deflections of plates
TL;DR: In this article, simplified equations for the deflection of uniformly loaded circular and rectangular plates with various boundary conditions are derived and compared with available numerical solutions of the exact equations, and the deflections found by this approach are then used to obtain the stresses, and resulting stresses are compared with existing solutions.
Journal ArticleDOI
Influence of Large Amplitudes on Flexural Vibrations of Elastic Plates
TL;DR: In this paper, approximate solutions for the nonlinear bending vibrations of thin plates are presented for the cases of rectangular and circular plates subjected to various boundary conditions, and the effects of large amplitudes on both the free and forced vibrations are clarified.