P. Lafortune, P. Terriault, V. Brailovski, C. Fischer-Rousseau, Ecole de technologie superieure, Montreal, QC, Canada; V. Torra, Polytechnical University of Catalonia, Barcelona, Spain
Shape memory alloy (SMA) dampers have been used in several applications due to their high reliability without requiring a continual monitoring. Unfortunately, several aspects related to SMA dampers need to be further analyzed. In this paper, a cantilever beam with two SMA wires working in opposition is dynamically loaded by a harmonic displacement of the fixed end while the displacement of the free end is measured. The effect of prestraining the SMA wires and the thermal effect related to the phase transformation are the phenomena being studied for different loading frequencies. The harmonic displacement is generated by a conventional testing machine while the displacement is monitored by a laser measuring sensor. Finite element simulations are also carried out and validated by the experiments. Prestrained SMA wires seem to provide better damping properties than unprestrained wires, but preliminary experiments point out a temporal evolution of the SMA properties that should be considered with cautiousness.
Summary: Recent publications demonstrate the benefits of using shape memory alloy (SMA) dampers to reduce the amplitude of deformation of structures dynamically loaded by a seism. Unfortunately, these studies do not bring a deep understanding of the phenomena involved. For example, it is difficult to conclude on the causes of the damping improvements (energy dissipation due to the intrinsic hysteresis of SMA, modification of the overall stiffness of the system due to the varying stiffness of SMA, etc.). In order to reach a better understanding, the work presented in this paper adopts a more systematic approach based on numerical and experimental analyses in which the dynamic loading is, instead of a seism, a harmonic displacement.
The structure being analyzed is a steel cantilever beam with an added mass at its free end. The system is excited by the motion of the support point (the fixed end) with a sinusoidal motion at different frequencies. A conventional testing machine is used for this purpose and a laser sensor measures the displacement of the mass. Also, two SMA dampers are introduced in the system. The dampers are simply SMA wires that connect the free end of the beam and the support at a given angle. The dampers work in opposition so that when one wire is being loaded, the other one is being unloaded.
In parallel, the exact same cases are numerically analyzed using ANSYS finite element simulation software and validated by the experiments. The SMA behaviour is a bilinear model that has been implemented in ANSYS using the user-defined feature called USERMAT. The numerical results are in good agreement with the experiments, indicating that they can be relied on with confidence. Finally, additional simulations are carried out to study the influence of the thermal effects related to the phase transformation. The thermal exchanges of the SMA wires with the environment are programmed inside the USERMAT routine in order to quantify their influence on the damping properties of the SMA wires. Both numerical and experimental results clearly show that these thermal effects modify the mechanical behaviour of the damper. Fortunately, from a modeling point of view, the calculation of the temperature variations in the SMA wires can be avoided if the material constants representing the dynamic response of the material are supplied to the finite element program instead of the quasi-static ones.
