Analytic Model of the Deflection of Piezoelectric Unimorph and Bimorph Structures with Numerical Verification

The constitutive equations of multi-layered piezoelectric structures are derived in a new form. In this form, the electromechanical coupling is presented as an additional stiffness matrix. This matrix is a true property of the piezoelectric structure and is independent of specific mechanical boundary conditions that may apply to the structure. A novel model of the electromechanical response of such structures is presented. This model accounts for the 3D kinematics of the structure deformation. Solution of example problems using the new model shows excellent agreement with full 3D finite element simulations. These solutions are also compared with the results of previous 2D model approximations presented in literature, and the inaccuracies associated with these previous models are discussed