Vibrations and Dynamic Response of Membranes With Arbitrary Shape

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Abstract
This paper deals with vibration and dynamic response problems of an arbitrary-shaped membrane subjected to general dynamic loads. The exact solution for an equation of motion in terms of general dynamic loads is used, and the boundary conditions of the membrane are satisfied by means of the Fourier expansion method. The results of free vibration and dynamic response problems are shown in generalized forms for arbitrary-shaped membranes. As examples of these problems, free vibrations of elliptical and crescent-shaped membranes and dynamic responses of elliptical membranes to annular impact loads are discussed by applying the Laplace transform method. For some typical cases, the results obtained are compared with those of the exact method.

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