Modeling of SMA Tendons for Active Control of Structures

The use of shape memory alloy (SMA) wires as active tendons to reduce vibra-tion of a building model is analytically investigated. Approximate dynamic equations for one bay of a multi-story building with SMA tendons are derived based on laws of thermodynamics and Brinson's constitutive equations. These equations are used to provide comparisons between us-ing SMA tendons passively and active for vibration control. In this model, the modes of transfor-mation considered are austenite to martensite (and detwinned martensite), martensite to detwinned martensite and martensite to austenite. In the active case, the wire opposing the direc-tion of the floor mass displacement is heated by passing a current through it to take advantage of the thermomechanical properties of SMAs. The current to a wire is shut off as soon as the tendon is 100% austenite. In the passive case, no current is supplied to the wire. A numerical integration program was developed to include internal and potential energy changes, input work into the ten-dons, and energy transfers associated with the latent heat of transformation. In this program, for numerical stability of the subroutine used, the current is shut off to the tendon as soon as the martensite volume fracture of that tendon goes below 0. 1%. Displacement profiles are presented for both the passive and active implementations of the SMA wire. Simulation results show a fac-tor of twelve improvements in steady state tracking error between the first floor and the base of the model structure when the tendons are used passively. The results are further improved by a factor of seven when the tendons are used actively. Also the effect of different cooling rates is ex-amined. Comparing tracking errors for the system using free convection and convection coeffi-cients of 80 and 100 W/m ² K, it is shown that lower cooling rates can result in a reduction in tracking error.