Exact solution for dynamic response of an elastic elliptical membrane

The elaborated method of eigenfunction expansion in terms of transcendental Mathieu and modified Mathieu functions is employed to present the first known exact time-domain series solution for transverse vibrations of a uniform elastic membrane of elliptical shape under arbitrary loading and initial conditions. Numerical calculations for displacement time response of an elliptical membrane of typical aspect ratio excited by various common types of transient loads are presented and discussed. Limiting cases are considered and good agreements with available results are obtained.