Modeling and deformation characteristics of a circular beam with asymmetric piezoelectric actuators

An analytical modeling of a circular curved beam with asymmetric surface-bonded piezoelectric actuators is developed in the paper. A circular unimorph with small curvature consists of a thin elastic layer and a thin piezoelectric layer. The unimorph is equivalent as a single layer structure, its static governing equation of the radial displacement is derived based on one-dimensional beam theory, the general solution of the equation is also given. From the general analysis of the beam actuated by multiply distributed actuators, some explicit expressions on the deflection of a cantilever unimorph and a cantilever beam with one distributed actuator are obtained. In numerical examples, both the FEM results and the straight unimorph chosen as a special case are used to validate the present model. Subsequently, the deformation characteristics of the actuator-driven beams are investigated by examining the effect of the different geometric setups of the beam systems on the deflection. Importantly, it is found that the variation trends of the radial displacement responses strongly depend on the central angles representing the location of the actuator and length of the elastic beam. The critical value of the central angle of the elastic beam is only dependent on the central angel of the actuator. It is hoped that the present modeling may be taken as the reference for the design and control of the curved smart structures.