Vibration analysis of the plates subject to distributed dynamic loads by using spectral element method

A spectral element method (SEM) is introduced for the vibration analysis of rectangular plates under distributed dynamic loads. In this paper, the spectral plate element matrix (often called the dynamic stiffness matrix) is formulated from the relation between the forces and displacement along the opposite two parallel edges. The distributed dynamic load is discretized into a sequence of equivalent line loads. The plate is then considered as a connection of two spectral plate element with the joint node line along which the equivalent line load acts. The spatial coordinate dependence of each equivalent line load is then removed through the spatial Fourier transformation so that the plate (2-D) problem becomes a simplified equivalent beam like (1-D) problem. The remaining solution procedures is therefore the same as that used for beam problems. Numerical tests show that the present SEM provides very accurate solutions when compared to finite element solutions.