Complex Boundary Conditions Of Arbitrary Shape Of The Plate Vibration Analysis

This paper gives a new analytical solution of the free vibration of an arbitrary-shaped plate with complex boundary conditions. The natural frequency equation is derived by using the Nagaya's Fourier expansion method^[31][41]. Then, the roots of the frequency of the equation can be numerically worked out by using computer. Because the general solution exactly satisfies the differential equations of the thin plate, the method can give the results with high precision. The calculating cost is little, the course of the analysis is rather simple.As the application and exactitude of the present method, numerical calculations have been carried out for square plates, circular plates with the mixed boundary conditions. The numerical results demonstrate the well convergence and high accuracy of the present method.