Journal ArticleDOI
Large amplitude flexural vibration of rectangular plates
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TLDR
By using an approximate formulation due to Berger, it was shown that the vibration of rectangular plates with large amplitudes may be treated in a simple and unified manner as mentioned in this paper, and numerical results were given for various boundary conditions.About:
This article is published in International Journal of Mechanical Sciences.The article was published on 1963-12-01. It has received 108 citations till now. The article focuses on the topics: Vibration & Boundary value problem.read more
Citations
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Finite element displacement method for large amplitude free flexural vibrations of beams and plates
TL;DR: 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.
Journal ArticleDOI
Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates
TL;DR: In this paper, the nonlinear thermomechanical vibration behavior of viscoelastic nanoplates is investigated based on nonlocal elasticity theory, and the geometrical nonlinearity is modeled while governing equations are solved applying semi-analytical differential quadrature method (DQM).
Journal ArticleDOI
On certain inconsistencies in berger equations for large deflections of plastic plates
J.L. Nowinski,H. Ohnabe +1 more
TL;DR: In this article, it is shown that the method may lead to grave inaccuracies and even become meaningless if the edge of the plate is free to move in in-plane directions.
Journal ArticleDOI
An investigation into the vibration analysis of a plate with a surface crack of variable angular orientation
R. Ismail,Matthew P. Cartmell +1 more
TL;DR: In this article, an analytical approach for the forced vibration analysis of a plate containing a surface crack of variable angular orientation, based on three different boundary conditions, is presented for the plate containing the angled surface crack with respect to one side of the plate.
Journal ArticleDOI
Nonlinear electroelastic vibration analysis of NEMS consisting of double-viscoelastic nanoplates
TL;DR: In this article, the nonlinear electroelastic vibration behavior of viscoelastic nanoplates is investigated based on nonlocal elasticity theory, and the geometrical nonlinearity is modeled while governing equations are derived through Hamilton's principle and they are solved applying semi-analytical generalized differential quadrature (GDQ) method.
References
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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
The Normal Modes of Nonlinear n-Degree-of-Freedom Systems
TL;DR: In this article, a system of n masses, equal or not, interconnected by nonlinear "symmetric" springs, and having n degrees of freedom is examined, and the problem of finding normal modes is reduced to a geometrical maximum-minimum problem in an n-space of known metric.
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.
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