Flexural Motion of Elastically Supported Rectangular Plates under Concentrated Moving Masses and Resting on Bi-Parametric Elastic Foundation

Abstract

Vibration analysis of plate-type structural member subjected to travelling masses and under elastically supported boundary conditions is considered in the present study. The specific aim of this work is to investigate the effects of elastically restrained boundary conditions and other vital structural parameters on the dynamic characteristics of structure-mass systems. An approximate analytical solution technique is employed to treat this problem. In particular, a technique based on separation of variables is used to reduce the governing equation of motion to a sequence of second order ordinary differential equations. The Struble’s technique and the integral transformations are thereafter employed to obtain solutions of the second order ordinary differential equations. Approximate analytical solutions for structure-load force and structure-load mass systems are obtained and discussed. Influence of some vital structural parameters on the dynamical system is established. Results show that, the effect of the shear modulus is more greatly pronounced than that of the foundation modulus; hence, it could be dangerous to rely on the design based on Winkler foundation which neglects completely the effect of shear modulus. Comparison was made between the dynamic deflection of the structure for the moving force and moving mass models. Effects of the mass ratio U0 on the dynamic stability of dynamical system are also established.