Eigenfrequencies of membranes of arbitrary boundary and with varying surface mass density

摘要

In this paper a boundary point collocation method is presented to solve the Helmholtz equation for the vibrations of membranes with varying surface mass density. Parameters contained in the general solution of the equation are used to satisfy homogeneous boundary conditions on a given boundary curve. These parameters are the eigenfrequencies, separation constants and the partial amplitudes of partial solutions.