Accurate analytical type solutions for the free in-plane vibration of clamped and simply supported rectangular plates

Highly accurate analytical type solutions are obtained by means of the superposition method for the free in-plane vibration frequencies and mode shapes of fully clamped rectangular plates. The modes are separated into three distinct families and each family is handled separately. Excellent agreement is encountered when computed results are compared with results obtained by other methods. Following the obtaining of solutions for the fully clamped plate, it is shown how this work can be exploited to obtain exact Levy type solutions for the free in-plane vibration modes of the plate with simple support along all edges. The pure shear and extensional vibration modes characteristic of the latter plate problem are handled separately. Again, excellent agreement with results obtained by other means is encountered. A limited number of mode shapes for the fully clamped plate are presented.