Vibration analysis of a single-layered graphene sheet embedded in visco-Pasternak’s medium using nonlocal elasticity theory

The vibration analysis of a single-layered graphene sheet (SLGS) embedded in viscoelastic medium is presented by using the nonlocal elasticity theory. The medium is considered by adding the damping to the usual foundation model which characterized by the linear Winkler’s modulus and Pasternak’s (shear) foundation modulus. The governing dynamical equation is obtained and solved for simply-supported SLGSs. The effects of many parameters like nonlocal parameter, aspect ratio, Winkler-Pasternak’s foundation, damping coefficient, and mode numbers on the vibration frequencies of the SLGSs are investigated in detail. The present results are compared with the corresponding available in the literature. Additional results are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak’s parameters for future comparisons.