Journal ArticleDOI
Large amplitude flexural vibration of simply supported skew plates.
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TLDR
In this article, the Berger formulation was applied to the large amplitude flexural vibration of orthotropic skew plates in the Berger regime and the results were compared with those obtained without making use of the approximate formulation due to Berger.Abstract:
Using the governing dynamic equations for the large amplitude flexural vibration of orthotropic skew plates in the Berger formulation, solutions are obtained on the basis of a one term vibration mode and they are discussed for two types of in-plane edge conditions and for different skew angles and orthotropy. The results obtained are compared with those got without making use of the approximate formulation due to Berger. In all these cases it is found that the nonlinearity is of the hardening type, i.e., the period of nonlinear vibration decreases with increasing amplitude.read more
Citations
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Nonlinear vibrations of a clamped rectangular plate with initial deflection and initial edge displacement— Part II: Experiment
N. Yamaki,K. Otomo,M. Chiba +2 more
TL;DR: Theoretical analyses for nonlinear vibrations of a clamped rectangular plate under a uniformly distributed periodic load, with the effect of both initial deflection and initial edge displacement taken into consideration, are presented in this paper.
Journal ArticleDOI
Non-linear vibrations of a clamped circular plate with initial deflection and initial edge displacement, part I: Theory
N. Yamaki,K. Otomo,M. Chiba +2 more
TL;DR: In this paper, the effect of both initial deflection and initial edge displacement on axisymmetric non-linear vibrations of a clamped circular plate of isotropic materials, under uniformly distributed lateral loading, with the effect taken into consideration.
Journal ArticleDOI
Analysis of dynamic instability for arbitrarily laminated skew plates
Guan-Yuan Wu,Y.S. Shih +1 more
TL;DR: In this paper, the dynamic instability and nonlinear response of rectangular and skew laminated plates subjected to periodic in-plane load are studied, and the region of dynamic instability associated with the effect of the stacking sequence of lamination and the skew angle of plate are also investigated and discussed.
Journal ArticleDOI
Non-linear flexural vibrations of anisotropic skew plates
Gangan Prathap,T.K. Varadan +1 more
TL;DR: In this article, the large amplitude free flexural vibrations of thin, elastic anisotropic skew plates are studied by using the von Karman field equations in which the governing non-linear dynamic equations are derived in terms of the stress function and the lateral displacement.
Journal ArticleDOI
On the berger approximation: A critical re-examination
TL;DR: 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.
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
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.
Journal ArticleDOI
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.
Journal ArticleDOI
Large-amplitude oscillations of oblique panels with an initial curvature
TL;DR: In this article, the Von Karman field equations for flexible oblique plates with an initial curvature are extended to a dynamical case using series of initial and additional deflections and Galerkin's procedure, the governing equation for an admissible mode time function is established using this single assumed modal deflection, and assuming built-in edge fiee to move in the inplane directions.
Journal ArticleDOI
Non-linear flexural vibration of orthotropic skew plates
M. Sathyamoorthy,K.A.V. Pandalai +1 more
TL;DR: In this article, the large amplitude (non-linear) free flexural vibration of thin, elastic, orthotropic skew plates clamped along all four edges was analyzed using the Galerkin's method.
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