Free vibrations of non-homo geneous circular and annular membranes

A non-homogeneous membrane is a membrane that has variable thickness or mat erial density. Several recent publications deal with the axisymmetric and a ntisymmetric modes of transverse vibration for a composite doubly connected and solid membrane with constant or variable density. In this paper, exact solutions for both the axisymmetric and antisymmetric modes of circular an d annular membranes with any piecewise polynomial variation of the density are given using a power series solution. The dynamic problem is solved exac tly using a recurrence relationship up to any accuracy desired, by deriving the dynamic stiffness matrix for circular and annular membrane elements. M any results for linear, parabolic, and cubic variation of complete and annu lar membranes are solved using the dynamic stiffness method and presented i n the Tables. (C) 2001 Academic Press.