Damped forced vibration of functionally graded porous sandwich plate

This study investigates the dynamic response of functionally graded (FG) porous viscoelastic sandwich plates with various porosity distributions under dynamic loading, an area that remains underexplored in existing literature. The plate considered in the analysis consists of a homogeneous ceramic core layer and upper and lower layers made of functionally graded porous material. The plate's displacements are described utilizing higher order shear deformation theory (HSDT). The motion's equations are derived utilizing Hamilton's principle and analytically solved through Navier approach. To streamline the solution process, displacements obtained in Laplace domain are converted back to the time domain utilizing Durbin's approach. A key novelty of this study lies in the incorporation of viscoelastic material properties, which are represented utilizing linear standard viscoelastic model. A computational code is developed in Mathematica to carry out the analyses. The developed code is verified by conducting FG porous sandwich plates' free vibration analysis and validating the results through comparison with studies in literature. Following this, a detailed parametric investigation is carried out by applying dynamic distributed loads to FG porous viscoelastic sandwich plate with various porosity distributions. Damped forced vibration analyses are carried out, examining the influences of viscoelastic damping ratios, porosity and porosity distributions, layer characteristics, and FG material gradations on the plate's displacement-time response and maximum displacements.