Journal ArticleDOI
Large amplitude free flexural vibrations of thin plates of arbitrary shape
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TLDR
In this paper, a finite element formulation for analyzing large amplitude free flexural vibrations of elastic plates of arbitrary shape is developed for analyzing stress distributions in the plates, deflection shape and nonlinear frequencies.About:
This article is published in Computers & Structures.The article was published on 1979-08-01. It has received 26 citations till now. The article focuses on the topics: Stiffness matrix & Finite element method.read more
Citations
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A finite element method for nonlinear forced vibrations of rectangular plates
Chuh Mei,Kamolphan Decha-Umphai +1 more
TL;DR: In this article, a harmonic force matrix of a rectangular element under uniform harmonic excitation was developed for nonlinear forced vibration analysis, where inplane deformation and inertia were both considered in the formulation.
Journal ArticleDOI
Buckled plate vibrations and large amplitude vibrations using high-order triangular elements
T. Y. Yang,A. D. Han +1 more
TL;DR: In this article, a high-order triangular membrane finite element is combined with a fully conforming triangular plate bending element to solve the geometrically nonlinear problems of plates where the membrane and flexural behaviors are coupled and the effect of the inplane boundary conditions is as significant as the flexural boundary conditions.
Journal ArticleDOI
A reinvestigation of post-buckling behaviour of elastic circular plates using a simple finite element formulation
TL;DR: In this paper, a modified finite element formulation to study the postbuckling behavior of elastic circular plates is presented and a discussion on the derivation of nonlinear stiffness matrix for post-buckling analysis is included and the present results are compared with continuum solutions.
Journal ArticleDOI
Buckling, postbuckling, and nonlinear vibrations of imperfect plates
Rakesh K. Kapania,T. Y. Yang +1 more
TL;DR: In this article, the incremental and total stiffness matrices for large displacement behavior are derived based on the total Lagrangian approach in conjunction with the Hamilton's principle, and the results obtained in this study are compared with existing solutions and a good agreement is seen.
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Certain discussions in the finite element formulation of nonlinear vibration analysis
B.S. Sarma,T.K. Varadan +1 more
TL;DR: In this paper, the finite element formulation and equivalent linearization technique used in the study of nonlinear vibrations of beams have been reexamined based on the earlier comments and errors present in the equivalent linearisation procedure, in the substitution of inplane boundary conditions at the element level instead of at the system level, and in the use of different connotation for the frequency, are discussed.
References
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Book
The finite element method in engineering science
TL;DR: In this paper, the authors describe how people search numerous times for their favorite books like this the finite element method in engineering science, but end up in malicious downloads, and instead they cope with some infectious bugs inside their computer.
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.