VIBRATION OF PLATES OF VARIABLE THICKNESS

Abstract

The present thesis is an attempt to study the free and forced vibrations of non-uniform polar orthotropic circular plates with elastically restrained edge. The whole range of the subject of study has been divided into eight chapters. The Chapter I gives an introduction to vibrational problems of plates with complicating effects such as elastic foundation, in-plane force and an loading presentingkup-to-date survey of literature dealing with free and forced vibrations. In chapter II, an analysis of asymmetric vibration of polar orthotropic circular plates of linearly varying thickness (LVT) with elastically restrained edge has been presented. Chapter Ill deals with axi-symmetric as well as asymmetric vibration of circular plates with parabolically varying thickness (PVT). In chapter IV the effect of an elastic foundation on the dynamic response of polar orthotropic circular plates of linearly as well as parabolically varying thickness has been studied. The results for classical boundary conditions i.e. clamped, free and'simply supported edge conditions have been obtained as particular cases of elastically restrained edge conditions. Chapter V presents an analysis of elastic stability and vibration of circular plates with. linear thickness variation. Chapter VI analyses -the combined effect of in-plane force and elastic foundation on vibration of polar orthotropic circular plates. The last two chapters i.e. chapters VII and VIII deal with forced vibration of polar orthotropic circular plates of linear as well as parabolic thickness variations in absence and presence of elastic foundation respectively. Since an analytical solution for vibration of plates of variable thickness is difficult to obtain, a number of research workers have used various numerical techniques such as finite difference, finite element, quintic splines, Chebyshev polynomials, generalised orthogonal polynomials, differential quadrature and Recepta.nce methods etc.