Nonlinear Analysis of a Flexible Beam Actuated by a Couple of Active SMA Wire Actuators

There are two different ways of using SMA wires as actuators for shape control of flexible structures; which can be either embedded within the composite laminate or externally attached to the structure. Since the actuator can be placed at different offset distances from the beam, external actuators produce more bending moment and, consequently, considerable shape changes with the same magnitude of the actuation force comparing to the embedded type. Such a configuration also provides fast convection which is very important in shape control applications that require a high-frequency response of SMA actuators. Although combination and modeling of externally-attached SMA actuator wires and strips have been considered by many researchers, these studies have some weaknesses neglecting them yields a number of errors between theoretical and experimental results. In this work, the aforementioned limitations of attaching actuators to the smart structures have been removed and a flexible beam actuated by two active SMA actuators is nonlinearly modeled. The Brinson constitutive equations and thermoelectric equations for SMA materials are coupled with the nonlinear beam behavior and the coupled system of equations is numerically solved for some particular practical cases. The analysis method done in this paper can be easily extended to the complicated smart structure with externally-attached SMA wires.