Vibration response of visco-elastically coupled double-layered visco-elastic graphene sheet systems subjected to magnetic field via strain gradient theory considering surface stress effects

Abstract

Based on strain gradient theory with surface effect, this article discusses magneto-vibration of coupled double-layered visco-elastic graphene sheet systems embedded on elastic foundation. Graphene sheets were placed in uniform magnetic field and coupled with each other by an enclosing visco-Pasternak medium. Considering the Kirchhoff plate theory and Kelvin–Voigt model, the governing equation is derived using Hamilton’s principle. The equation is solved analytically to obtain the frequency of the coupled system. The parametric study is thoroughly performed, concentrating on the series effects of a magnetic field, visco-elastic damping structure coefficient, aspect ratio, surface layer, visco-Pasternak elastic medium, shear modulus, and mode number. In this system, in-phase and out-of-phase vibrations are investigated. The numerical results of this article show a perfect correspondence with those of the previous researches. The effect of magnetic field on the vibration of graphene sheet with different Winkler coefficients is exposed. Results from the model demonstrate that the magnetic field increases the natural frequencies.