Investigation of Flexoelectric Effect on Nonlinear Vibration and Dynamic Instability of Piezoelectric Sandwich Micro/Nanobeam Using the Nonlocal Strain Gradient Theory

Abstract

A size-dependent electromechanical Euler–Bernoulli micro/nanobeam is proposed to address the nonlinear vibration and instability regions on the basis of nonlocal strain gradient theory (NSGT) and von-Karman hypothesis. The micro/nanopiezoelectric sandwich beam is axially influenced by the parametric excitation. Moreover, the electric enthalpy energy density is employed to consider the effect of flexoelectricity. The nonlinear equations of motion are derived with the aim of Hamilton’s variational approach. In this study, the electrostatic and Casimir forces are considered. The multiple time scales method is employed to solve the equation. Based on the outcomes of this research, it can be claimed that the flexoelectric and piezoelectric parameters have a pivotal influence on the amplitude response and dynamic instability regions. Furthermore, the applied voltage enlarges the distance between the bifurcation points and has a softening effect on micro/nanobeam. This work tries to provide a comprehensive understanding of flexoelectric micro/nanosandwich beam and prepare valuable information for designing flexoelectricity-based micro/nanostructures such as actuators, sensors, switches and resonators.