Thermo-mechanical stability of single-layered graphene sheets embedded in an elastic medium under action of a moving nanoparticle

Using an energy-based method, this paper sought to analyze dynamic stability and parametric resonance of single-layered graphene sheets (SLGSs) embedded in thermal environment and elastic medium while carrying a nanoparticle moving along an elliptical path. In order to present a realistic model, all inertial effects of the moving nanoparticle are taken into account in the dynamic formulation of the system. Equations governing the transverse vibrations of the embedded SLGS are obtained using the Hamilton's principle. Small-scale effects based on the Eringen's nonlocal elasticity theory are considered in deriving the motion equations. The equations governing the reduced model are calculated based on the Galerkin method. To calculate the instability boundaries, the energy-rate method is applied on the ordinary differential equations (ODEs) governing the system oscillations. The effects of nonlocal parameter, the nanoparticle motion path radii, SLGS length-to-width ratio, temperature change of the thermal environment, stiffness of the elastic medium and boundary conditions of SLGS on the parametric instability regions are examined. The results show that these parameters influence the system stability, so that a decrease in the nonlocal parameter, the SLGS length-to-width ratio and the nanoparticle motion path radii and also an increase in the stiffness coefficients of the elastic medium improve the system stability. The model presented in this paper is validated by comparing the observations with those published in previous studies.