Free transverse Vibration analysis of rectangular plate with multiple line-concentrated mass using DQEM

In this paper, the transverse vibration of a rectangular plate with multiple line concentrated masses is investigated by using differential quadrature element method (DQEM). Governing equation and boundary and compatibility conditions are formulated based on differential quadrature rules. The boundary conditions are simply supported in the direction of width of plate and arbitrary in the direction of its length. The compatibility conditions at the position of concentrated mass are assumed as the continuity of transverse displacement, rotation and bending moment and discontinuity in the transverse force due to the acceleration of the concentrated mass. The effects of number, magnitude and position of the masses and boundary conditions on the value of natural frequency are investigated. The accuracy, convergence and efficiency of the proposed method are confirmed by comparing the obtained numerical results with the exact solutions of the other researchers