Asymmetrically laminated piezoelectric bars

A theory of arbitrary laminated electroelastic bars is constructed. The influence of the electrical conditions on the faces of piezoelectric layers is taken into account in the constitutive relations of electroelasticity. It is shown that, in general, the problem for bars of asymmetrical structure is not divided into a plane problem and a bending problem. It is shown that the rotary inertia should be taken into account in the equations of motion in the neighbourhood of the natural vibration frequencies of the bar. A way of simplifying the solution of the problem is found by an asymptotic method. After solving the problem for a laminated bar, formula that enable one to change from one-dimensional required quantities to three-dimensional quantities are obtained. As an example, the vibrations of a two-layer electroelastic bar are considered, and displacements, stresses and electrical quantities are calculated, and also the dependence of the electromechanical coupling coefficient on the vibration frequencies and the thicknesses of the elastic and piezoelectric layers is studied.