Buckling and postbuckling analysis of rectangular plates resting on elastic foundations with the use of the spectral method

2012 ◽  
Vol 205-208 ◽  
pp. 213-220 ◽  
Author(s):  
Aliki D. Muradova ◽  
Georgios E. Stavroulakis
Keyword(s):  
Spectral Method ◽  
Rectangular Plates ◽  
Elastic Foundations

scholarly journals Three-dimensional free vibration of thick plates with general end conditions and resting on elastic foundations

2018 ◽  
Vol 38 (1) ◽  
pp. 110-121
Author(s):  
Zhuang Lin ◽  
Shuangxia Shi
Keyword(s):  
Boundary Conditions ◽  
Ritz Method ◽  
Three Dimensional ◽  
Series Representation ◽  
General Boundary ◽  
Geometrical Parameters ◽  
Penalty Function Method ◽  
Rectangular Plates ◽  
General Boundary Conditions ◽  
Elastic Foundations

This paper presents a three-dimensional formulation for the free vibrations of thick rectangular plates with general boundary conditions and resting on elastic foundations. The general boundary conditions are imposed by means of penalty function method. The displacements of the plates are expressed by a three-dimensional cosine series and some simple polynomial functions which introduced to ensure and accelerate the convergence of the series representation. All the unknown coefficients can be obtained by using the Rayleigh–Ritz method. Comparisons of the present results with those in available literature demonstrate the accuracy and reliability of the present formulation. Furthermore, parametric investigations are presented including the effects of boundary conditions, geometrical parameters, and elastic foundation.

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