Non-linear Frequency Response and Stability Analysis of Piezoelectric Nanoresonator Subjected to Electrostatic Excitation

Abstract

The effects of surface energy on the non-linear frequency response and stability analysis of piezoelectric cylindrical nano-shell as piezoelectric nanoresonator are investigated in the current paper using Gurtin–Murdoch surface elasticity and von Karman–Donnell’s theory. The nanoresonator is embedded in visco-Pasternak medium and electrostatic excitation. The governing equations and boundary conditions are derived using Hamilton’s principle and also the assumed mode method is used for changing the partial differential equations into ordinary differential equations. Complex averaging method combined with arc-length continuation is used to achieve an approximate solution for the steady-state vibrations of the system. The validation of the mentioned system is achieved with excellent agreements by comparison with numerical results. The parametric studies such as the effects of geometrical and material properties, different boundary conditions, the ratio of length to radius $L/R$ for different values of the voltages ${V_{{\rm{DC}}}}$ and ${V_{{\rm{AC}}}}$, the gap width of the nanoresonator $b/L$, the effect of the voltages ${V_{{\rm{DC}}}}$ and ${V_{{\rm{AC}}}}$ and also the effect of piezoelectric voltage ${V_p}$ are conducted on the non-linear frequency response and stability analysis of the piezoelectric nanoresonator.

Nonlinear vibration and stability analysis of double-walled piezoelectric nanoresonator with nonlinear van der Waals and electrostatic excitation

“…In order to study the steady state response of the system, the complexification-averaging method is applied (Hashemi Kachapi et al, 2019a and 2019b; Manevitch and Manevitch, 2005). For each mode of motion, complex variables are introduced to the following form…”