Quasi-3d Shear Deformation Theory for the Vibration Study of Viscoelastic FGM Nanoplates Resting on Visco Winkler-Pasternak Substrate Medium

This study provides an analysis of the free vibration of functionally graded nano-plates with variable parameters resting on viscoelastic foundations using quasi three-dimensional shear deformation theory. The plate is assumed to be made of a functionally graded material with visco-elastic behavior resting on a visco-elastic foundation to reduce the vibration of the plate. The scaling effect is induced by Erigin’s nonlocal model and Kelvin–Voigt’s visco-elastic behavior are applied to define the equilibrium equations of the system. A new shear function is proposed to calculate the fundamental frequencies. A detailed parametric study is then carried out to examine the effects of non-local parameters, the viscoelastic foundation and internal damping on the vibration characteristics of the visco-elastic nano-plates are also presented and discussed in detail. The present solutions are in good agreement with those found in the literature. We note that the various parameters studied in this work have a significant effect on the durability of the structure.