Magnetoelectric effects in laminated multiferroic shells

Two-dimensional equations for laminated multiferroic shells of piezoelectric and piezomagnetic layers are obtained from the exact three-dimensional equations. Mechanically, the two-dimensional equations represent the so-called first-order theory that describes coupled extensional, flexural and thickness-shear motions. The electric and magnetic fields are described layer by layer. The two-dimensional equations obtained are used to study magnetoelectric coupling in a laminated multiferroic circular cylindrical shell. Both static coupling and the frequency dependence of the coupling in time-harmonic motions are examined.