Modeling considerations for in-phase actuation of actuators bonded to shell structures

Abstract

A closed-form model to represent the in-phase actuation of induced strain actuators bonded to the surface of a circular shell is developed. Because of the inherent shell curvature, the equivalent discrete tangential forces generally used to represent the in-phase actuation of the actuators (such as in pin-force models) are not colinear and result in the application of rigid body forces on the shell. This nonequilibrium state violates the principle of self-equilibrium of fully integrated structures, such as piezoelectrically actuated shells. The solution to this nonequilibrium problem is to apply a uniform transverse pressure over the actuator region to maintain equilibrium. Using this adequate equivalent loading scheme for in-phase actuation, a response model for a circular ring is derived based on shell governing equations. To verify the in-phase actuation response model, finite element analysis is performed. A perfect match between the in-phase actuation response model and the finite elements results, when the actuator mass and stiffness are neglected, validates the derived analytical model. If the self-equilibrium is not maintained (point-force model), the predicted deformed shape is completely different from the actual shell response to in-phase actuation. Thus, by simply applying a uniform transverse pressure along with the discrete tangential forces to maintain the self-equilibrium of the shell, the shell response can be modeled accurately.