Pseudoelastic SMA radius size effects on the damping of structural vibrations

The design of pseudoelastic shape memory alloy (SMA) passive damping devices for structural vibration is dependent on the geometry of the SM. By changing the effective radius size of an attached SMA element, one simultaneously changes the nonlinear stiffness and damping contributed to the system by the SMA. In order to identify the coupled nonlinear dynamic behavior, this work focuses on the steady state frequency response functions of a simple SDOF system with an attached SMA element under base excitation. An equivalent linearization method is used to produce a qualitative representation of the frequency response of the structure for multiple radius sizes and excitation amplitudes. These results are then compared to corresponding frequency response functions produced from the Seelecke, Muller, and Achenbach SMA model. These results give insight into jump phenomenon, hysteretic damping effects, and identify the stable branches of the nonlinear frequency response. Additionally, optimal radius sizes are presented for a range of harmonic excitation amplitudes and frequencies. These results lead to an initial investigation into the physical mechanisms responsible for choosing optimal radius sizes for an arbitrary excitation.