The dynamic behaviour of piezoelectric laminated bars

A theory of laminated electroelastic bars with layers arranged symmetrically about the middle plane of the bar is constructed. Particular attention is given to the influence of the electrical conditions on the faces of the piezoelectric layers on the equations of the theory of bars. Formulae are obtained which, after solving the problem of a laminated bar, enable one to transfer from one-dimensional required quantities to three-dimensional required quantities. As an example, the vibrations of a three-layer electroelastic bar are considered, the displacements, stresses and electrical quantities are calculated, and the dependence of the electromechanical coupling coefficient on the frequency of the vibrations and the thicknesses of the elastic and piezoelectric layers is investigated.