AXISYMMETRICAL VIBRATIONS OF SOLID CIRCULAR AND ANNULAR MEMBRANES WITH CONTINUOUSLY VARYING DENSITY

The present paper reports the results from a series of numerical exper iments dealing with the determination of the lower natural frequencies for the transverse vibration of annular membranes (including the spec ial case of a solid circular membrane) when the mass per unit area var ies linearly, quadratically, and cubically with the radial co-ordinate . The frequency coefficients have been determined using: (1) the diffe rential quadrature method; (2) the finite element technique; (3) an op timized and/or improved Rayleigh quotient method; and (4) a lower boun d based on the Stodola-Vianello method. Excellent agreement is achieve d among the different methodologies. (C) 1998 Academic Press Limited.