Analytical modeling and static response of a curved beam with imperfectly bonded piezoelectric actuators

An analytical description of the static characterization of a curved beam with surface-bonded piezoelectric transducers is developed in this paper. The uniform curved beam is thin and actuated by distributed piezoelectric patches. The governing equations of these structures with small curvature are derived based on one-dimensional beam theory. The static analysis of the beam actuated by multiply distributed PZT patches is then given in detail based on a transfer matrix method. Furthermore, the actuation mechanism of the piezoelectric patches is also investigated, considering the effects of the interfacial shear stresses between the piezoelectric patches and the host elastic beam. Then, parametric studies on the static characteristics of the beam are performed to examine the effects of the parameters: applied electric field, the thickness and length of the PZT wafers and the thickness of bonding layers etc. Finally, an analytical expression reflecting the relation between the external load and electric voltage is established for the displacement control problem.