The Pin-Force Model Revisited

Abstract

The pin-force model is one of the earliest models developed for beams actuated in bending. In this model, the actuators and substrates are considered as separate elastic bodies and the forces from the actuators are transferred to the substrates by "pins" at the edges of the actuators. Although this model of force transfer is consistent with the assumed perfect bonding scenario, where the shear stress is concentrated in a small area close to the edge of the actuator, it fails to provide the correct structural response for the case where the actuator is relatively thick. In this paper, while retaining the basic features of this model (i.e., treating the actuator and beam as separate bodies), the corrections necessary to upgrade this model to the level of the more accurate Bernoulli-Euler model are presented. The basic difference lies in the appropriate inclusion of the actuator flexural stiffness in the structural moment-curvature equations. Two configurations are considered: one in which the actuators are symmetrically bonded on the surface of the beam and activated out-of-phase, and one in which the actuator is bonded to one side of the beam only. The static beam response equa tions developed for both cases are shown to be identical to those obtained from the more rigorous Bernoulli-Euler model. This work thus forms a bridge between the relatively simple pin-force model and the Bernoulli-Euler model, and illustrates the use of mechanics principles in the treatment of structures with active members such as induced strain actuators.