Eigenvibration for the Membrane between Two Eccentric Circles

Abstract

The solutions of the wave equation for a membrane bounded by fixed two eccentric circles are obtained. By the aid of the addition theorem of the Bessel functions, the boundary condition on two circles is reduced to a set of homogeneous simultaneous linear equations, from which eigenvalues and eigenfunctions are obtained in power series of d (the distance between two centers). Some numerical results are obtained to the order of d⁶ or d⁴.