Vibrations of rectangular plates of bilinearly varying thickness and with general boundary conditions

Results are presented for the fundamental frequency of a rectangular plate having a thickness which varies in a bilinear fashion in the x-direction. Translational and rotational flexibilities are taken into account at all edges. A simple algorithm, which allows one to evaluate the fundamental frequency of vibration, is derived by making use of the Ritz method and expressing the fundamental displacement function in terms of a polynomial co-ordinate function which satisfies approximately the natural boundary conditions.