scholarly journals Solution of Rectangular Plate on Winkler’s Elastic Foundation Using Characteristic Orthogonal Polynomials

2020 ◽  
Vol 4 (8) ◽  
pp. 119-124
Author(s):  
  E. I. Ogunjiofor
Keyword(s):  
Orthogonal Polynomials ◽  
Rectangular Plate ◽  
Elastic Foundation

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

Static and Dynamic Buckling of a Compressed Narrow Rectangular Plate on an Elastic Foundation

2008 ◽  
Author(s):  
Leonid Srubshchik ◽  
Issac Herskowitz ◽  
Irina Peckel ◽  
Edward Potetyunko
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Isotropic Plate ◽  
Vertical Direction ◽  
Dynamic Buckling ◽  
Initial Time ◽  
Asymptotic Formulas ◽  
Surface Load ◽  
Small Surface ◽  
Asymptotic Values

In this paper we consider a thin narrow rectangular isotropic plate subjected to a small surface load and supported laterally by a continuous nonlinear elastic foundation. The both short ends of plate are clamped while the longitudinal sides are completely free, so that their points can move along the boundary, along the normal to the boundary, and in a vertical direction. At initial time the uniformly distributed in-plane compressive stresses are suddenly applied to the short ends in the longitudinal direction. Our goal is to find the asymptotic formulas for values of static and dynamic buckling load in the case of the narrow elastic plate and estimate their values as function of the imperfection parameter. We apply the geometrically nonlinear theory for the thin rectangular isotropic plate laterally supported by the continuous softening or stiffening foundation to formulate an associated nonlinear spectral problem for the load parameter. This problem contains a small natural parameter δ - the ratio of the width of the rectangular plate to its length and can be integrated using the asymptotic method developed in the work by Srubshchik, Stolyar and Tsibulin [1]. Accordingly we approximate the solution of the original problem by the leading term of the finite expansion in δ which is described by the motion equations of an axially compressed elastic column on the nonlinear continuous elastic foundation which has only one spatial dimension and can be investigated more comprehensively. The formulas for asymptotic values of the static and dynamic buckling compressive loads are obtained by means of the perturbation theory and by one-term Fourier’s approximation respectively. The specific numerical results for these asymptotic values are presented.

Free Vibration Analysis for Disconnected Thin Rectangular Plate with Four Free Edges on Nonlinear Elastic Foundation

2011 ◽  
Vol 52-54 ◽  
pp. 1309-1314 ◽  
Author(s):  
Yong Gang Xiao ◽  
Cui Ping Yang
Keyword(s):  
Free Vibration ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Vibration Analysis ◽  
Harmonic Balance Method ◽  
Free Vibration Analysis ◽  
Variation Principle ◽  
Thin Rectangular Plate ◽  
Nonlinear Elastic Foundation ◽  
Nonlinear Elastic

In this paper, the free vibration analysis of thin rectangular plate with dowels on nonlinear elastic foundation is investigated. The load transfer on dowels is modeled as vertical springs, whose stiffness depends on the dowel properties and the dowel-plate interaction. Based on Hamilton variation principle, the nonlinear governing equations of thin rectangular plate with discontinuities on nonlinear elastic foundation are established, and the suitable expressions of trial functions satisfying all boundary conditions are proposed. Then, the equations are solved by using Galerkin method and harmonic balance method. The numerical simulation reveals the effects of the dowel parameters and the other ones of the system on free vibration behaves of the disconnected thin rectangular plate.

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