Exact solution for thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium

Abstract

In this paper, the effect of the temperature change on the vibration frequency of mono-layer graphene sheet embedded in an elastic medium are studied. Using the nonlocal elasticity theory, the governing equations are derived for single-layered graphene sheets. Using Levy and Navier solutions, analytical frequency equations for single-layered graphene sheets are obtained. Using Levy solution, the frequency equation and mode shapes of orthotropic rectangular nanoplate are considered for three cases of boundary conditions. The obtained results are subsequently compared with valid result reported in the literature. The effects of the small scale, temperature change, different boundary conditions, Winkler and Pasternak foundations, material properties and aspect ratios on natural frequencies are investigated. It has been shown that the non-dimensional frequency decreases with increasing temperature change. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the nanoplates.

Hygrothermal deformation of orthotropic nanoplates based on the state-space concept

“…[20,22,23,26,27,46,48] represents a special case of the present twovariable plate theory when the shear displacement c¼0. …”

“…Jomehzadeh and Saidi [47] employed the first-order shear deformation plate theory to study the free vibration of an isotropic nanoplate using Levy type method. Recently, Mohammadi et al [48] studied the effect of the temperature change on the vibration frequency of SLGSs embedded in an elastic medium using Levy type solution based on CLPT.…”

Ritz Method in Vibration Analysis for Embedded Single-Layered Graphene Sheets Subjected to In-Plane Magnetic Field

“…Furthermore, the investigation regarding the embedded plate behavior includes the work of Akgöz and Civalek [22] (where the free vibrations of a single-layered graphene sheet resting on an elastic matrix as the Pasternak foundation are investigated), the work of Bastami [23] (where the nonlocal elasticity theory is used and the proposed approach is based on the Ritz method). Mohammadi [24,25] investigated thermo-mechanical vibrations and vibrations under the biaxial in-plane preload of orthotropic graphene sheet embedded in an elastic medium based on the nonlocal elasticity theory. Behfar and Naghdabadi in [26] studied vibrations of multi-layered nanoplates embedded into the elastic medium with the constant Van der Waals force acting between nanoplates.…”

Nonlocal vibration analysis of circular double-layered graphene sheets resting on an elastic foundation subjected to thermal loading

“…Bending, vibration, and buckling of rectangular and circular GSs have been studied by different researchers [24][25][26][27][28][29][30][31][32][33][34]. For example, Arash and Wang [35] investigated the vibration of single-and doublelayered graphene sheets (SLGSs and DLGSs) using the nonlocal elasticity theory and molecular dynamics simulations.…”