# Dynamic Response of an Elastically Connected Double Non-Mindlin Plates with Simply-Supported End Condition due to Moving Load

Document Type: Original Article

Authors

1 Department of Mathematics, University of Ilorin, Ilorin, Kwara-State, Nigeria.

2 Department of Mathematics, Ekiti - State University(EKSU), Ado-Ekiti, Ekiti - State, Nigeria.

Abstract

In this paper, the dynamic response of two identical parallel non-mindlin  (i.e., not taking  into account the effect of shear deformation and rotatory inertia) plates which are elastically connected and subjected to a constant moving load is considered. The fourth order coupled partial differential governing equations is formulated and solved, using an approximate analytical method by assuming; firstly, a series solution later on treating the resulting coupled second order ordinary differential equations with an asymptotic method of Struble. The differential transform method, being a semi-analytical technique, is applied to the reduced coupled second order ordinary differential equations, to get a non-oscillatory series solution. An after treatment technique, comprising of the Laplace transform and Pade approximation techniques, is finally used via MAPLE ODE solver to make the series solution oscillatory. The dynamic deflections of the upper and lower plates are presented in analytical closed forms. The effect of the moving speed of the load and the elasticity of the elastic layer on the dynamic responses of the double plate systems is graphically shown and studied in details. The graphs of the plate's deflections for different speed parameters were plotted. It is however observed that the transverse deflections of each of the plates increase with an increase in different values of velocities for the moving load for a fixed time $t$.

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