Effective Nonlocal TSDT for Free Vibration of FGM Sandwich Nanoplates Embedded in Kerr Foundation under Heat Conduction

Abstract

This research introduces a novel approach by applying the effective nonlocal parameter (ENP) through the third-order shear deformation theory (TSDT) for investigating the free vibration of a functionally graded material sandwich (FGM-SW) nanoplate embedded in a Kerr elastic foundation under heat conduction, solved numerically using Navier’s closed-form solution. In this study, an analytical model incorporates temperature-dependent (TD) material properties and nonlinear temperature distribution (NTD), which are formulated using the temperature functions and polynomial power series, respectively. The governing equations are derived using Hamilton’s principle for the FGM-SW nanoplate. The impact of different ENP, power-law index, temperature rise, elastic foundation, and the nonlocal parameter ratio on both low- and high-order frequency parameters is demonstrated. The results reveal that variations in the ENP significantly influence the frequency of the FGM-SW nanoplate model, with a more pronounced impact observed for ceramic-based ENP than for metal-based ENP. This distinction arises from the composition of the FGM-SW nanoplate, which comprises FGM skins and a ceramic core. Notably, the trends vary when the constant nonlocal parameter (CNP) is assumed for ceramic versus metal.

Keywords: Effective nonlocal parameter, constant nonlocal parameter, FGM-SW nanoplate, third-order shear deformation theory, Kerr foundation