Modeling of Shape Memory Alloy (SMA) spring elements for passive vibration isolation using simplified SMA model and Preisach model

Abstract

Advances in smart materials and structures technology, especially in applications of Shape Memory Alloys (SMA) as actuators and vibration isolation devices, require understanding of the nonlinear hysteretic response found in SMAs. SMA hysteresis can be modeled either through constitutive models based on physical material parameters or through models based on system identification. In this work, a simplified phenomenological model (motivated from SMA constitutive response) and a Preisach model (system identification based model) have been developed for predicting the non-linear, hysteretic, pseudoelastic force-displacement relationship of SMAs. Model calibration tests performed for both models have been discussed in detail. The SMA structures have been modeled as pseudoelastic spring elements, and the models have been utilized to solve a single degree of freedom (SDOF) pseudoelastic SMA spring-mass system. The effect of SMA pseudoelasticity on this SDOF dynamic system has been investigated for various loading levels and system configurations, and the importance of large amplitude motion has been discussed. Variable damping and tunable isolation response have been shown as major benefits of SMA pseudoelasticity. It has also been shown that SMA based devices can overcome performance trade-offs inherent in a typical softening spring-damper vibration isolation system. An efficient software tool for design and simulation of SMA based vibration isolation applications has been developed. The models have also been utilized to simulate a prototype SMA-based vibration isolation device, where SMA tubes have been used as isolators. Correlation of numerical simulations and experimental results has resulted in concluding that, for an SMA based vibration isolation device to be effective in reducing the transmissibility of a dynamic system, large amplitude displacement causing phase transformations of SMA devices is necessary. In terms of modeling, the Preisach model gave better numerical predictions of the experimental results due to close proximity of the Preisach model response to actual SMA tube behavior compared to the simplified model. However, for the generic parametric study conducted, the simplified model was found to be more useful as it was motivated from the constitutive response of SMAs and, hence, could easily incorporate different changes in system conditions.