Dynamic analysis of viscoelastic composite plates in the laplace domain

The present study aims to investigate the damped response of laminated Mindlin plates subjected to dynamic loads. The solutions of damped response of anti-symmetric, cross-ply and angle-ply laminates have been obtained by Finite Element Method (FEM) in conjunction with the Laplace transform method using the first order shear deformation theory. The governing equations of motion of the problem are first obtained in the time domain. Subsequently, Laplace transform is applied and the linear algebraic equations are solved numerically. Materials of the laminates are assumed linear elastic or viscoelastic. In the viscoelastic material case, the Kelvin model is employed. According to the correspondence principle the material constants are replaced with their complex counterparts in the Laplace domain. Therefore, the presented model incorporates damping very easily in the transformed domain. The solutions obtained are transformed to the time domain using the modified Durbin?s numerical inverse Laplace transform method. For the suggested model, a general-purpose finite element analysis computer program is coded in Fortran. Verification of the numerical procedure is performed by comparing the results of present method with semi-analytical results available in the literature. Obtaining the equation first discretely in the time domain using FEM and then applying the Laplace transform has proved to be a procedure highly accurate and efficient compared to other numerical methods available in the literature.