Axisymmetric vibrations of solid circular and annular membranes with continuously varying density

摘要

The present paper reports the results from a series of numerical experiments dealing with the determination of the lower natural frequencies for the transverse vibration of annular membranes (including the special case of a solid circular membrane) when the mass per unit area varies linearly, quadratically, and cubically with the radial co-ordinate. The frequency coefficients have been determined using: (1) the differential quadrature method; (2) the finite element technique; (3) an optimized and/or improved Rayleigh quotient method; and (4) a lower bound based on the Stodola-Vianello method. Excellent agreement is achieved among the different methodologies. (C) 1998 Academic Press Limited. [References: 10]