Nonlinear electromechanical analysis of micro/nanobeams based on the nonlocal strain gradient theory tuned by flexoelectric and piezoelectric effects

Abstract

This study investigates the size-dependent dynamic pull-in instability of piezoelectrically and electrostatically actuated micro/nanobeams considering the Euler–Bernoulli theory and von-Kármán hypothesis based on the nonlocal strain gradient theory. In this respect, the impacts of flexoelectricity and piezoelectricity are considered using electrical Gibbs-free energy density and the governing equation is acquired with the help of Hamilton's principle for a sandwich beam with elastic core and two piezoelectric layers. In the present model, different nonlinear forces, such as the fringing field, electrostatic, and intermolecular forces are taken into account. Then, the governing equation is converted from partial differential equation into ordinary one by the Galerkin method considering various boundary conditions, subsequently, the homotopy analysis method is applied as an analytical procedure. The results are validated by comparing the linear frequency, nonlinear frequency, and dynamic pull-in voltage with those in the literature. Consequently, the impacts of different parameters including piezoelectric voltage, nonlocal parameter, length scale parameter, initial amplitude, electrostatic force, flexoelectric, and gap to thickness ratio are discussed in detail.