Quasi-static and dynamic response of functionally graded viscoelastic plates

In this study, quasi static and dynamic response of functional graded material (FGM) viscoelastic plates under dynamic loads were investigated. The governing equations of composite plates were obtained with the help of Hamilton's principle. Afterwards, time dependent partial differential equations were obtained by applying Navier solution method to these valid equations. These equations were transformed into Laplace space in order to solve time dependent partial differential equations. The transformation of the resulting calculations from Laplace domain into the time domain was conducted with the help of Modified Durbin algorithm. The obtained results were compared with various approaches It was shown that the results are in parallel with other approaches' results, and in full agreement with the results of the finite element method (ANSYS). Then, quasi-static behavior was investigated for viscoelastic FGM because of there is not enough research on this subject. The sensitivity analysis demonstrated that the volume fractions and damping ratios have a significant effect on the quasi-static and dynamic response of viscoelastic FGM plates. The numerical sample results showed that the present method can solve the problem in a highly accurate, efficient, and easily by utilizing the Laplace transform without the use of natural frequencies or mode shapes.