Transient response of circular plates and membranes: A numerical approach

A systematic discussion on the use of numerical Laplace transforms for the computation of response of circular plates and membranes is presented. Applying the Laplace transform to the governing differential equation of motion in polar coordinates reduces the dynamic problem to an equivalent static one. The resulting equations are discretized by using the finite difference technique and the solution is obtained in the Laplace plane. Time-domain solutions are obtained by using the numerical inversion technique proposed by Durbin based on sine—cosine transforms. The effects of internal viscoelastic damping and external viscous damping on the response are also studied. Several examples are tackled to illustrate the procedure.