Pergamon 0020-7403(94) E0008-S Int, J. Mech.Sci. Vol. 36, No. 5, pp. 439-448, 1994 Copyright ~ 1994Elsevier Science Ltd Printed in Great Britain. All rights reserved 0020-7403/94 $6.00 + 0.00 FORCED AXISYMMETRIC RESPONSE OF LINEARLY TAPERED CIRCULAR PLATES A. P. GUPTA and NAVNEET GOYAL* Department of Mathematics, University of Roorkee, Roorkee 247667, India (Received 24 April 1993; and in revised form 28 October 1993) Abstract--Forced axisymmetric response of a circular plate of linearly varying thickness, based on the classical theory, is analyzed by the eigen-function method. An exact solution for the free vibration mode shapes is obtained by the Frobenius method. Clamped and simply-supported plates subjected to symmetric uniformly distributed and concentrated impulsive ring and point loads are solved as example problems. Numerical results computed for transverse deflection and radial stress are plotted in the figures. NOTATION a radius of plate fl taper constant p density of plate material 3'1,72 inner radius of uniformly loaded region )'o radius of concentrated impulsive ring load E Young's modulus v Poisson's ratio Fo total load on the plate Dimensionless R Ho H W T F ¢YR (Mg, Mo) quantities r/a, radial coordinate ho/a, thickness of plate at center h/a, thickness of plate w/a, transverse deflection t x/E/{pa2(1 - v2)}, time (1 - v2) f/E, external applied load/area (1 - v:)ar/E, radial stress (1 - v2)/(Ea2)(mr, m0), bending moments 1. INTRODUCTION The study of the dynamic response of engineering structures subjected to time-dependent loads has gained considerable importance in modern engineering and applied science. As structural elements of variable thickness are widely used in engineering structures to achieve lightness with strength, and sometimes to satisfy certain specific design requirements, it becomes important to know their dynamic response subjected to various time-dependent loads. In particular, it becomes desirable to study the dynamic response of circular plates of variable thickness as they are used in design of machine parts, e.g. diaphragms of steam turbines and pistons of reciprocating engines. The problem of forced motion of circular plates of constant thickness has been studied by a number of authors [1-6], but only a few researchers have analyzed the forced vibration of circular plates of variable thickness. Laura et al. [7] have considered static and dynamic behavior of circular plates of variable thickness elastically restrained along the edges. Greco and Laura 1-8] studied the forced vibration of a circular plate with thickness varying in a bilinear fashion. Some other recent papers on forced vibration of beams and plates of variable thickness are cited in Refs I-9-14]. In all the above references the force function is taken to be harmonic. *Author to whom correspondence should be addressed. 439