Size-dependent constituent equations of piezoelectric bimorphs

In this paper, two size-dependent constituent equations for symmetrical/heterogeneous piezoelectric bimorph actuators are developed using the modified couple stress theory and the principle of minimum total potential energy. The present model involves an internal material length scale parameter used to capture the size effect. In the limit when the internal material length scale parameter goes to zero, this model reduces to classical (local) constituent equations available in the literatures. Exact solutions for the normalized static deflection are obtained as a function of the ratio of the actuator thickness to the internal material length scale parameter. The simulations show that the static deflection developed by the present model has a remarkable difference with those got by the classical constituent equations when the ratio of the beam thickness to the internal material length scale parameter is small. It is also observed that the stiffness of elastic layers show directionally opposite effects on tip deflections of symmetrical piezoelectric bimorph actuator and heterogeneous one.