Transverse vibration of membranes of arbitrary shape by the method of constant-deflection contours

Abstract A method for approximate computation of the fundamental frequency of membranes of arbitrary shape vibrating harmonically is developed. The method is based upon the concept of contour lines of equal deflection on the surface of the membrane. A similar method for elastic plates has recently been developed by the author in a series of papers. As illustrations of the procedure, the method is applied to the calculation of the gravest mode of an annular, an elliptic, and a parabolic membrane.