Jump phenomena of rotational angle and temperature of NiTi wire in nonlinear torsional vibration

This paper performs experimental and analytical investigations on jump phenomena of thermomechanical responses of a nonlinear torsional vibration system with a phase transformable NiTi Shape Memory Alloy (SMA) wire as a nonlinear spring. By synchronizing the measurement of rotational angle and temperature of the NiTi wire in the torsional vibration system under external sinusoidal excitation, their evolutions in the transient and steady states are acquired. By monotonically increasing/decreasing the excitation frequency with small intervals around the primary resonance frequency, Frequency Response Curves (FRCs) of these two physical quantities are obtained and their jumps on the FRCs are captured in the frequency domain. To understand and quantify such jump phenomena, an effective Duffing oscillation model is introduced to simulate the mechanical behaviour of NiTi SMA in the dynamic system and to determine the FRCs and the characteristic jump frequencies. A lumped heat transfer analysis is then performed to establish the relationship between the temperature oscillation and the rotational angle. It is shown that the jump of the rotational angle is accompanied by a simultaneous jump of the temperature oscillation of the NiTi wire in torsional vibration. Particularly, the coupling effect between the thermal response and mechanical response can be significant and must be considered in the study of a nonlinear dynamic system with NiTi SMA component.