Vibration analysis of porous functionally graded nanoplates

Abstract

This paper deals with the free vibration analysis of porous functionally graded nanoplates (FGPNs) reinforced with graphene platelets (GPLs) resting on Visco-Pasternak foundation using the Navier method. The formulation is based on the first-order shear deformation theory (FSDT) and Hamilton’s principle. The material properties of FGPNs are supposed to be graded in the thickness direction based on a simple power-law function. The Halpin–Tsai model is used to predict the effective Young’s modulus of the GPL-reinforced nanocomposite in terms of GPL weight fraction and dimension. The small scale is considered based on Eringen’s nonlocal elasticity theory. Also, the Kelvin–Voigt model is used for the Visco-Pasternak foundation. A detailed parametric study is conducted to investigate the effects of various parameters such as porosity coefficient, GPL weight fraction, geometrical parameters, nonlocal parameter, Winkler and Pasternak foundations, and damping coefficients on the dimensionless natural frequencies of FGPNs. The results demonstrate that the natural frequency increases with increasing GPL weight fraction while decreases with increasing porosity coefficient. In addition, it is observed that ignoring the nonlocal parameter overestimates the natural frequencies of the FGPN. It is concluded that the proposed method is accurate and reliable by comparing the results with those of the previously published works. Therefore, this paper can be used as a benchmark for future studies on the vibration of FGPNs.