Journal ArticleDOI
On the berger approximation: A critical re-examination
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TLDR
In this article, a plausible explanation for the origin of the Berger method is suggested using certain well known results from the two dimensional theory of elasticity, and it is shown that such methods fail to predict the non-linear behaviour with respect to important parameters and that whatever accuracy is obtained in the solution of a particular problem can at best be attributed to fortuity.About:
This article is published in Journal of Sound and Vibration.The article was published on 1979-09-22. It has received 13 citations till now. The article focuses on the topics: Elasticity (economics).read more
Citations
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Journal ArticleDOI
Asymptotic approaches in mechanics: New parameters and procedures
Journal ArticleDOI
Geometrically nonlinear flexural response characteristics of shear deformable unsymmetrically laminated plates
TL;DR: In this paper, a higher-order shear deformation theory involving four dependent unknowns and satisfying the vanishing of transverse shear stresses at the top and bottom surfaces of the plate, thus avoiding use of shear correction factors, is employed for the study reported here.
Journal ArticleDOI
On the theory of berger plates
TL;DR: In this paper, it was shown that the Berger equations can be obtained on the basis of a sequential asymptotic procedure and the results of /1/ were later extended to orthotropic plates /2/, membranes /3,4/, shallow spherical /4,8/ and cylindrical /8,10/ shells.
Journal ArticleDOI
Large deflection analysis of cylindrical shells on a pasternak foundation
D.N. Paliwal,V. Bhalla +1 more
TL;DR: In this article, the effect of geometric, material and foundation parameters on load-deflection characteristics of a cylindrical shell on a Pasternak foundation was investigated for simply supported movable and immovable edge conditions.
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Effects of edge restraints on the non-linear flexural vibrations of an imperfect cross-ply laminated plate resting on an elastic foundation
TL;DR: In this paper, a solution for the non-linear Marguerre dynamic equilibrium and compatability equations for the large amplitude free flexural vibrations of an imperfect, cross-ply, laminated plate, having elastically restrained edges and resting on an elastic foundation is presented.
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.
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Large amplitude flexural vibration of rectangular plates
TL;DR: 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.
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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.
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A study of Berger equations applied to non-linear vibrations of elastic plates
TL;DR: In this article, the variationally derived in-plane boundary conditions are examined with specific reference to the plates with edges free of inplane stress resultants, and it is shown that for this boundary condition the Berger equations can result in zero nonlinearity.
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On the non-linear vibrations of rectangular plates
Gangan Prathap,T.K. Varadan +1 more
TL;DR: In this article, a solution based on a one-term mode shape, for the large amplitude vibrations of a rectangular orthotropic plate, simply supported on all edges or clamped on all corners for movable and immovable in-plane conditions, is found by using an averaging technique that helps to satisfy the inplane boundary conditions.