On the dynamic response of viscoelastic functionally graded porous plates under various hybrid loadings

This paper studies the dynamic out-of-plane and in-plane responses of a viscoelastic plate made of functionally graded porous (FGP) materials in a closed-form solution under various combinations of boundary conditions. Firstly, the FGP parameters of the plate are considered to vary along the thickness direction based on distinct nonlinear porosity distributions. Secondly, the first-order shear deformation theory (FSDT) of elasticity, the energy technique, and the calculus of variations are employed to obtain the governing equations of motion. Thirdly, to account for structural damping, the derived equations are extended to constitutive equations using the standard linear solid (SLS) model. Finally, the system of partial differential equations with variable coefficients is analytically solved using the perturbation approach. To do so, the equations with variable coefficients are transformed into a system with constant coefficients by introducing a new parameter, and the lateral dynamic response is determined in a closed-form solution with no approximation. In addition to time-dependent transverse loads, namely transient and impulsive loads, different space-dependent load profiles of constant, linear, parabolic, and sine distributions are also applied on the plate surface. Furthermore, by inserting solution-dependent material properties, a user-defined field (USDFLD) code is provided to evaluate the accuracy of the analytical results in Abaqus/Standard analysis.