Pull-in instability and nonlinear vibration analysis of electrostatically piezoelectric nanoresonator with surface/interface effects

Abstract

In current study, nonlinear dynamics and stability analysis of piezoelectric nanoresonator (PENR) based on cylindrical nanoshell is investigated using the Gurtin–Murdoch surface/interface (S/I) theory. The piezoelectric nanoresonator is simultaneously subjected to direct voltage DC and alternating voltage AC. For this analysis, Hamilton′s principles, the assumed mode method combined with Lagrange–Euler′s are used for the governing equations and boundary conditions. Complex averaging method combined with arc-length continuation is used to achieve the effect electrostatic and piezoelectric voltages and other parameters on pull-in voltage, nonlinear frequency response and stability region of the piezoelectric nanoresonator. It is found that the mentioned parameters can effectively change the flexural rigidity of the system which in turn affects the pull-in instability regime and nonlinear frequency response. The obtained results show that, by changing the surface/interface densities for nanoresonator (NR) and PENR and as a result, increasing or decreasing the system stiffness, the natural frequency can be lower or greater than the case of without S/I effects. Also near the natural frequency of the nanoshell, softening or hardening types of nonlinear behavior, the jump phenomenon and saddle-node bifurcation are presented. The effect of different parameters on nonlinear dynamics and stability analysis of piezoelectric nanoresonator (PENR) is also examined.