Method for solving vibration problems of a plate with arbitrary shape

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Abstract
This paper is concerned with a method for solving vibration problems of a thin elastic plate with arbitrary shape. The exact solution of an equation of motion is utilized and the boundary conditions along both arbitrarily shaped curved and straight line boundaries are satisfied by means of the Fourier expansion method. Numerical calculations are carried out for the clamped or simply supported elliptical and parabolic plates.

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