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

Control and analyze the nonlinear dynamic stability of single layered graphene sheets (SLGSs) integrated with zinc oxide (ZnO) actuators and sensors are the main contributions of present work. In order to present a realistic model, the material properties of system are assumed viscoelastic using Kelvin–Voigt model. The surrounding elastic medium is simulated with nonlinear orthotropic visco-Pasternak foundation. Considering refined zigzag theory (RZT), a new formulation is developed through the Gurtin–Murdoch elasticity theory in which the effects of surface stress are incorporated. A novel numerical procedure namely as differential cubature (DC) method is applied for solution. A proportional-derivative (PD) controller is used for the active control of the system dynamic stability. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, magnetic field, viscoelastic foundation, surface stress, applied voltage, controller and structural damping on the dynamic instability region (DIR) of system. The accuracy of the proposed method is verified by comparing its numerical prediction with other published works as well as solution of system with differential quadrature (DQ) and harmonic differential quadrature (HDQ) methods. Results depict that the magnetic field and external voltage are effective controlling parameters for DIR of system.