Nonlinear Vibration and Stability Analysis of Rotating Functionally Graded Piezoelectric Nanobeams

Abstract

Presented herein is an investigation for the nonlinear vibration and stability analysis of rotating functionally graded (FG) piezoelectric nanobeams based on the nonlocal strain gradient theory. The present model can be regarded as a simplified version for the rotating nanowire of biomechanical nanogenerators. The Hamilton principle is used to derive nonlinear equations of motion and their related boundary conditions, which are then discretized to form a set of algebraic equations. Accordingly, the nonlinear vibration frequencies and buckling loads of the nanobeams can be determined by an iterative method. A parametric study of rotational velocity, nonlocal parameter, material length parameter, power-law index, and electrostatic voltage on the dynamic stability behavior of such nanobeams is also presented. In the cantilever case, increasing the nonlocal parameter and material length parameter can result in a stiffness-hardening effect that is unaffected by rotational velocity and the material length parameter to nonlocal parameter ratio. Yet, this has not been reported previously. More importantly, incorporating the effect of geometric nonlinearity on the dynamic responses and stability results of the nanobeams is indispensable. In particular, new observations for the coupling effect of vibration amplitude and power-law index on the electric potential effect are useful for the design of rotating microelectromechanical devices.