Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM

Abstract

In this paper, a nonlocal continuum plate model is developed for the transverse vibration of double-piezoelectric-nanoplate systems (DPNPSs) with initial stress under an external electric voltage. The Pasternak foundation model is employed to take into account the effect of shearing between the two piezoelectric nanoplates in combination with normal behavior of coupling elastic medium. Size effects are taken into consideration using nonlocal continuum mechanics. Hamilton׳s principle is used to derive the differential equations of motion. The governing equations are solved for various boundary conditions by using the differential quadrature method (DQM). In addition, exact solutions are presented for the natural frequencies and critical electric voltages of DPNPS under biaxial prestressed conditions in in-phase and out-of-phase vibrational modes. It is shown that the natural frequencies of the DPNPS are quite sensitive to both nonlocal parameter and initial stress. The effects of in-plane preload and small scale are very important in the resonance mode of smart nanostructures using piezoelectric nanoplates.