Dynamic Response of a Membrane With Both Curved and Straight Line Boundaries

In this paper a method for solving vibration and dynamic response problems of a membrane having an arbitrary shaped boundary consisting of curved and straight lines is presented. The frequency equation for the arbitrary-shaped membrane is given, and the solution for the membrane subjected to general transient load is obtained in a generalized form. As a numerical example, the response of a parabolic membrane subjected to a uniformly distributed exponentially decaying load is investigated.