The effects of nonlocal and surface/interface parameters on nonlinear vibrations of piezoelectric nanoresonator

Abstract

In current work, Gurtin–Murdoch surface/interface and nonlocal theories are presented to investigate nonlinear vibration and stability analysis of piezoelectric nanoresonator simultaneously subjected to direct and alternating voltages. Complex averaging method combined with arc-length continuation is used to achieve the nonlinear frequency response and stability analysis of the piezoelectric nanoresonator. It is concluded that ignoring surface and small-scale effects lead to inaccurate results in vibration response of the piezoelectric nanoresonator. Also, with increasing dimensionless nonlocal parameter and decreasing nanoshell stiffness, dimensionless natural frequency, the resonance amplitude, the range of instability with saddle-node bifurcations and nonlinear hardening behavior, and also resonance frequency decrease. In addition, it is found that when the surface/interface effects corresponding to higher surface/interface density are considered, natural frequency is increased. Also, regardless the Lamé’s constants lead to decreasing of piezoelectric nanoresonator stiffness, and as a result, the dimensionless natural frequency is lower than all cases. The rest of the surface/interface parameters do not have much effect on the dimensionless natural frequency. Also, with increasing electrostatic and piezoelectric voltages, the oscillation amplitude and range of the piezoelectric nanoresonator system’s instability and all nonlinear behavior of piezoelectric nanoresonator are increased.