Coupled Thermomechanical Dynamics of Phase Transitions in Shape Memory Alloys and Related Nonlinear Phenomena

Abstract

The aim of this paper is to study the coupled non-linear dynamics of the behaviour of Shape Memory Alloys (SMA) under harmonic excitation. The thermomechanical model developed by Falk and based on Landau theory is used to describe the coupled thermomechanical behaviour of the SMA mass-damper-bar system. Fully coupled mechanical and thermal field equations are established to reveal the strong coupling phenomena arising from the phase transition. Then, the harmonic balance method is used to obtain the steady-state frequency responses. The effect of thermomechanical coupling on the frequency and time response curves is taken into account by modifying the heat transfer coefficient. The results show that deformation and temperature provide a stable sinusoidal response. The analysis of the results leads to different ways of controlling the nature and extent of the coupled and non-linear response of SMA-based oscillators. Comparison of the analytical results with experimental data from the literature validates the coupled thermomechanical nonlinear model. These results can be used effectively to control the external vibrations of various systems.