Free Vibration Analysis of Rectangular Thin Plate With Multiple Openings Under General Boundary Conditions

The free vibration characteristics of a rectangular thin plate with series of openings are studied based on the Rayleigh-Ritz method in this paper. Firstly, the strain energy and kinetic energy of the plate are calculated utilizing the modified Fourier series. Then, uniformly distributed transitional and rotational springs are applied to deal with general boundary supports, and the elastic potential energy of the springs can be obtained. Furthermore, the plate is divided into several parts according to its amounts of openings and the energy of each parts are calculated separately and the spring stiffness of cut line between two separated parts are the same. Finally, the governing equation of the plate is obtained with the energy functional variation method. The present method is proved to be accurate by comparing the natural frequencies with those calculated by the finite element method. Besides, the influence of the amounts of openings and the area of total openings are discussed.