Investigation of dynamic behaviour of circular plates resting on Winkler and Pasternak foundations

Abstract

Investigating the dynamic behaviour of circular plate resting on elastic foundations are very important in designing of structural systems. This study examines the free vibration analysis of circular plate resting on Winkler and Pasternak foundations. The governing nonlinear partial differential equation is transformed to Duffing equation based on von Kármán geometric nonlinear principle and the nonlinear to linear frequency ratios are obtained while the linear natural frequencies are determined using Galerkin of weighted residual method. Also, the accuracy and reliability of the approximate solutions obtained are demonstrated by comparing the obtained results with available results reported in the literature. The analytical solutions obtained are used for examining the effect of elastic foundations on the dynamic behaviour of the circular plate. From the results, it is observed that, increasing elastic foundation parameter increases the natural frequency. As the nonlinear foundation increases, the nonlinear vibration frequency ratio decreases. The nonlinear Winkler foundation attenuates the amplitude of vibration of the circular plate. It is hoped that, the present study will contribute to the existing knowledge of classical theory of vibration.

Axisymmetric Bending of Circular Plates on a Variable Elastic Base

“…Some studies are devoted to the dynamics issues. Thus, in [5] a threedimensional analysis of the free vibrations of circular plates supported on foundations according to the Pasternak model with different boundary conditions is presented. A semi-analytical approach using the method of the space of states in the thickness direction and the method of one-dimensional differential quadratures in the radial direction is used to obtain the influence of the Winkler elasticity coefficients and the shear layer of foundations on the dimensionless natural frequencies of annular plates.…”

Construction of an algorithm to analytically solve a problem on the free vibrations of a composite plate of variable thickness

“…The free vibrations of an annular plate on elastic support according to the Winkler-Pasternak hypothesis were considered in [17]. Natural frequencies were determined by the Galerkin method.…”