A one-dimensional model for dynamic analysis of generally layered magneto-electro-elastic beams

A new one-dimensional model for the dynamic problem of magneto-electro-elastic generally laminated beams is presented. The electric and magnetic fields are assumed to be quasi-static and a first-order shear beam theory is used. The electro-magnetic problem is first solved in terms of the mechanical variables, then the equations of motion are written leading to the problem governing equations. They involve the same terms of the elastic dynamic problem weighted by effective stiffness coefficients, which take the magneto-electro-mechanical couplings into account. Additional terms, which involve the third spatial derivative of the transverse displacement, also occur as a result of the piezoelectric and/or piezomagnetic behavior. It is also shown that the magnetoelectric inputs can be treated as equivalent external axial forces and bending moments per unit length. Free vibrations and frequency response solutions are presented to validate the model by comparing the present results with those found in the literature or obtained by finite element analysis. Based on the successful validation of the model, new results for free vibrations of functionally graded magneto-electro-elastic beams are presented.