Analytical solution for Magneto-Electro-Elastic Bimorph

In this paper an analytical model for Magneto-Electro-Elastic bimorph beam with transverse electric and magnetic poling directions is presented. The model is based on the Euler-Bernuolli’s beam theory and on the assumption that the electric and magnetic field component along the beam length can be neglected. Starting from the gradient and divergence equations written for the magneto-electric fields, the expressions of the electric and magnetic scalar potentials are first derived in terms of the magneto-electric boundary conditions and of the beam curvature. Then a forth order ordinary differential equation governing the mechanical behavior of the magneto-electro-elastic beam is derived and solved for some particular magneto-electro-mechanical schemes