Variational-based modeling of a piezoelectric/elastic bilayer beam with flexoelectricity

Abstract

Flexoelectricity incorporating electric polarization and strain gradients exists in all dielectrics. In the present work, the function of Hamilton’s principle of the elastic dielectric materials considering the flexoelectric effect is established and its stationary conditions are also obtained. A bilayer beam composed of elastic and piezoelectric parts is modeled to investigate flexoelectricity under both mechanical and electrical loads. Based on Hamilton’s principle, the governing equation and boundary conditions of a piezoelectric/elastic bilayer beam with generalized supporting ends are deduced. Accordingly, the analytical solutions to the horizontal displacements are derived. It is found that the flexoelectric effects depend on the size heavily, which is dominant for the structures at nanoscale but had hardly influence on the larger ones. Moreover, the piezoelectric/elastic bilayer beam behaves much better on controlling of the bending flexibility by adjusting the thickness ratio of the two parts. It’s hopeful to provide guidance for designing and optimizing nanoscale electronic devices.

Keywords:

• Flexoelectric effect
• variational principle
• electromechanical coupling
• piezoelectric material
• size effect