Dynamics of piezoelectric laminae under a bias

The macromechanical analysis of the dynamics of a piezoelectric laminae under a mechanical bias within the effective stiffness concept of laminated composites is discussed. The piezoelectric laminae consists of arbitrary numbers of perfectly bonded layers, each with a distinct but uniform thickness, curvature, and electromechanical properties. It is coated with very thin electrodes on both of its faces. The fundamental equations of a piezoelectric strained medium are expressed by the Euler-Lagrange equations of a unified variational principle. A set of two-dimensional, approximate equations of the piezoelectric laminae is established. A direct method of solution is indicated for the macromechanical analysis and certain special cases are considered. The governing equations are derived in invariant Lagrangian form and accommodate all the types of motions of the biased piezoelectric laminae. All the significant effects, both mechanical and electrical, are taken into account