Modeling of the bilayer piezoelectric microbeam based on the strain gradient effect

Abstract

In this paper, a size-dependent bilayer piezoelectric microbeam model is established based on the modified piezoelectric theory, which considers the strain gradient effect. The hypothesis of the Euler–Bernoulli beam is taken for the size-dependent bilayer piezoelectric microbeam model. The governing equations and boundary conditions are obtained from the variational principle. The electromechanical coupling performance for two boundary value problems of a cantilever beam and a simply supported beam is assessed. The size dependence of a bilayer piezoelectric microbeam electromechanical coupling property under the direct piezoelectric effect and converse piezoelectric effect is investigated. Results reveal that, for the piezoelectric mircobeam, the electromechanical coupling responses have been restrained by the size effect. The induced charge and deflection predicted by the size-dependent model is smaller than that of the classical model. However, the influence of the size effect is weakened with the increase in the beam thickness. The size effect can be neglected when the beam thickness is far greater than the material length-scale parameter. Because the structural stiffness of the cantilever beam is higher than that of the simply supported beam, the electromechanical coupling responses of the bilayer piezoelectric cantilever microbeam are greater than that of the bilayer piezoelectric simply supported microbeam.