Wave approach for the resonances of rectangular and triangular membranes

Abstract

This study develops a ray technique for determining the resonance frequencies of triangular membranes. The technique is demonstrated for homogenous rectangular and triangular membranes with fixed boundaries. Where possible, the results are compared with exact calculations. The membrane resonances are calculated using an equivalent string whose length is proportional to the reciprocal of the length of closed paths starting from an arbitrary point within the membrane. Closed paths are ray paths which arrive back at the starting point going in the same direction.