Nonlinear thermo-nonlocal vibration and instability analysis of an embedded single-layered graphene sheet conveying nanoflow using differential quadrature method

Abstract

In this study, transverse nonlinear vibration and instability analysis of a viscous-fluid-conveyed single-layered graphene sheet (SLGS) subjected to thermal gradient are investigated. The small-size effects on bulk viscosity and slip boundary conditions of nanoflow through Knudsen number ( Kn), as a small size parameter is considered. Viscopasternak model is considered to simulate the interaction between the graphene sheet and the surrounding elastic medium. Continuum orthotropic plate model and relations of classical plate theory are used. The nonlocal theory of Eringen is employed to incorporate the small-scale effect into the governing equations of the graphene sheet. Differential quadrature method is employed to solve the governing differential equations for simply supported edges. The convergence of the procedure is shown and the effects of flow velocity, temperature change and aspect ratio on the frequency of the single-layered graphene sheet are investigated. Moreover, the critical flow velocities and the instability characteristic are determined. It is evident from the results that the natural frequency of nanosheet increases with rising temperature.

Visco-surface-nonlocal piezoelasticity effects on nonlinear dynamic stability of graphene sheets integrated with ZnO sensors and actuators using refined zigzag theory

“…Free vibration of SLGS resting on Pasternak foundation medium was investigated by Akgöz and Civalek [13] using the modified couple stress theory. Nonlinear vibration and instability analysis of a viscous-fluid-conveyed SLGS subjected to thermal gradient were investigated by Ghorbanpour Arani et al [14]. Nonlocal vibration analysis of the coupled system of double DLGSs embedded in a Visco-Pasternak foundation was carried out by Ghorbanpour Arani et al [15] based on DQ method.…”

Thermo-mechanical vibration, buckling, and bending of orthotropic graphene sheets based on nonlocal two-variable refined plate theory using finite difference method considering surface energy effects

“…23 Among all size-dependent theories, the nonlocal elasticity theory has been commonly applied in the theoretical investigations of structures at small scale. [24][25][26][27][28][29][30][31][32][33] Both atomistic simulation results and experimental observations on phonon dispersion have demonstrated the accuracy of nonlocal theory assumption. 23 Based on lattice dynamics and MD simulations, Chen et al 34 provided an atomic viewpoint to study microcontinuum field theories, including micro-morphic, micro-structure, micro-polar, Cosserat theory, couple stress, and nonlocal theories.…”

Electro-magneto wave propagation analysis of viscoelastic sandwich nanoplates considering surface effects

“…Their results indicated that when the value of additional material length scale parameter increases, the values of natural frequencies and buckling loads increase while the deflection decreases. Nonlinear thermo-nonlocal vibration and instability analysis of an embedded single-layered graphene sheet conveying nanoflow using differential quadrature (DQ) method were investigated by Ghorbanpour Arani et al 14 Nonlocal vibration analysis of the coupled system of double DLGSs embedded in a Visco-Pasternak foundation was carried out by Ghorbanpour Arani et al 15 based on DQ method. Shi et al 16 investigated the study on wave propagation characteristics of double-layered graphene sheets via nonlocal Mindlin-Reissner plate theory.…”