Nonlinear vibration analysis of viscoelastic micro nano-composite sandwich plates integrated with sensor and actuator

Due to the numerous applications of the laminated structures in micro-electro-mechanical systems (MEMS), the existence of the sensor and actuator at the top and bottom surfaces can increase the performance of such structures. In this research, the nonlinear vibration behavior of a smart micro sandwich plate is studied. The core of the micro structure is a viscoelastic three-layer polymeric composite plate reinforced by carbon nanotubes (CNTs) which is integrated by viscoelastic piezoelectric layers subjected to electric field. The piezoelectric layers at the top and bottom surfaces of the structure play the role of the actuator and sensor, respectively. The micro structure is embedded in the viscoelastic medium which is simulated by visco-Pasternak model. The piezoelasticity theory is applied to capture the small-scale effect and the Kelvin model is used to consider the viscoelastic behavior of the structure. Since the surface to bulk ratio of the micro structures is high, so the surface stresses are considered by employing the Gurtin–Murdoch theory. By applying the energy method and Hamilton’s principle, the governing equations of the structure are derived based on the zigzag theory. Finally the nonlinear frequency of the system is obtained using the differential quadrature method and the effects of various parameters like small-scale, surface stress, visco-Pasternak medium, electric fields and composite layers on the nonlinear vibration of the smart micro sandwich structure are examined. Results indicate that with increasing volume percent of CNTs and considering surface effects lead to higher frequency.