Effects of Shear Deformation and Rotary Inertia on the Dynamics of a Simply Supported Anisotropic Plates Traversed by a Distributed Moving Force

Abstract

The effects of shear deformation and rotary inertia on the dynamics of an anisotropic plate resting on a bi-parametric Vlasov foundation and traversed by a distributed moving force is investigated in this work. The Mindlin plate model is used as the basis for the mathematical model of an anisotropic plate having a varying flexural rigidity and varying density. Galerkin’s weighted residual method is employed to reduce the fourth order governing partial differential equation into a set of coupled fourth order ordinary differential equation which is solved using the Laplace transform method. The method required expressing the Heaviside function that represent the distributed moving load on the structure as a Fourier sine series. A closed form solution is obtained for the problem of anisotropic plate on a Vlasov foundation subjected to a moving distributed force. Results obtained with the aid of MATLAB programming indicate that shear modulus and rotary inertia correction factor all have significant influence on the anisotropic plate. It was observed that increasing the shear modulus and rotary inertia of the plate reduced the amplitude of displacement of the plate. Shear deformation and rotary inertia should not be neglected in models and solutions involving the dynamics of anisotropic plates traversed by moving distributed forces as this could lead to serious defects in bridges, roads, decking and machine parts.