Modeling of magnetoelectric composite nano-cantilever beam with surface effect

This work investigates the magnetoelectric response of a magnetostrictive–piezoelectric composite nano-cantilever beam with consideration of surface effects through the surface-layer-based model. The magnetoelectric composite nano-cantilever is treated as a bulk core plus two surface layers. The influences on the cantilever’s overall properties resulted from the surface effect is modeled as a spring force exerting on the boundary of the bulk core. A Kirchhoff’s theory is used to get the explicit solutions for the magnetoelectric effect of cantilever when subjected to bias magnetic field loads. In order to apply the appropriate boundary conditions on the cantilever, the effective axial force, shear force and moment are derived. Using the derived results, the so-called effective Miller–Shenoy coefficient, static and electromechanical resonance properties of the ME composite nano-cantilever beam for the extensional–bending coupling deformations are analyzed theoretically. At the same time, the effect of the substrate on ME effect is theoretically studied by altering the thickness of the substrate. The results indicate that the surface effects play a significant role in the magnetoelectric response of the ME composite nano-cantilever beam. This work is very helpful for design of nano-cantilever beam based devices and understanding the size-dependent properties of nanostructured ME composites in nano-electromechanical systems.