VIBRATION OF ORTHOTROPIC CIRCULAR AND ELLIPTIC PLATES RESTING ON ELASTIC FOUNDATION

Abstract

Lot of work is available in the literature on vibration of isotropic plates of constant thickness having simple geometries like rectangular and circular. Comparatively less work is available on anisotropic circular plates of varying thickness. That too is depending on one parameter. The purpose of the present investigation is to fill the gap upto some extent, The thesis deals with the determination of frequencies, nodal lines and mode shapes for free flexural vibrations of circular and elliptic plates having one dimensional quadratic and two dimensional linear and other variations in thickness, made up of orthotropic material and resting on Winkler elastic foundation. All the problems are analyzed by using boundary characteristic orthonormal polynomials in Rayleigh-Ritz method. Frequencies and mode shapes for various normal modes of vibration are computed by Jacobi method for free, simply supported and clamped boundary conditions. Frequencies are presented in tables whereas mode shapes are shown in figure. Convergence of frequencies at least upto five significant figures is discussed. Comparison in particular cases are made with the results already available in the literature. A close agreement is found in almost all the cases. In most of the cases our results are found to be better even for less number of terms in the solution. Chapter I, is devoted to introduction and survey of the work available so far in the literature on circular and elliptic plates of constant or variable thickness made up of isotropic or orthotropic material and subjected to other effects. Information in brief about the present work is also given in this chapter. Conclusion derived from the present work is given in Chapter X. The rest of the thesis is divided into two parts. Part-I deals with the vibration of circular plates and comprises Chapter II to V. Part-Il deals with the vibration of elliptic plates and comprises Chapter VI to IX.