Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part I: Governing equations and reciprocal relationships

A piezoelectric laminate theory that uses the piezoelectric phenomenon to effect distributed control and sensing of bending, torsion, shearing, shrinking, and stretching of a flexible plate has been developed. This newly developed theory is capable of modeling the electromechanical (actuating) and mechanoelectrical (sensing) behavior of a laminate. Emphasis is on the rigorous formulation of distributed piezoelectric sensors and actuators. The reciprocal relationship of the piezoelectric sensors and actuators is also unveiled. Generalized functions are introduced to disclose the physical concept of these piezoelectric sensors and actuators. It is found that the reciprocal relationship is a generic feature of all piezoelectric laminates.