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

Abstract

a b s t r a c tThis 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.

Forced synchronization of periodic and aperiodic thermoacoustic oscillations: lock-in, bifurcations and open-loop control

“…Like the V-shaped lock-in curve and the 'shark-fin' frequency-response curve, the jump phenomenon has been observed in various nonlinear systems, such as electronic circuits (Giannakopoulos & Deliyannis 2001), hypoid gears (Wang & Lim 2011), ecosystems (Scheffer et al 2001), shape-memory alloys (Xia & Sun 2015) and turbulent premixed combustors (Bellows et al 2008). Crucially, it can be modelled accurately with a forced Duffing oscillator, a second-order nonlinear damped oscillator with cubic elasticity subjected to periodic forcing (Nayfeh & Balachandran 2004):…”

Grain size effects on stability of nonlinear vibration with nanocrystalline NiTi shape memory alloy

“…Replacing b by q and a (b q a q p = + = + A ft sin 2 ), we have The steady-state response is obtained through the method of multiple scales heat analysis (see [6,7] for more details) is performed to establish the relationship between temperature oscillation (DT ) and rotation ( q D ) of the NiTi bar, and c , eq thermal response of the nonlinear dynamic system further involves specific latent heat (l 0 ) of the nanocrystalline material.…”

“…When NiTi SMA is used as a nonlinear damping component, such instability manifests as the jump phenomena of thermomechanical responses from one branch of solution to the alternative branch in the frequency and amplitude domains as shown in figure 1(c) [6,7]. When deformation of NiTi SMA is in softening nonlinear phase transition stage, the smooth and stable dynamic response along one branch of frequency response curve (FRC) or amplitude response curve (ARC) will gradually go into a metastable region and eventually become unstable and drastically switch to a contrasting alternative stable state along the other branch of FRC or ARC.…”

Frequency-Domain Bifurcation Analysis of a Nonlinear Flight Dynamics Model

“…A smooth variation in input frequency could then, for example, cause abrupt changes in both amplitude and phase, known as jump phenomena. Forced oscillation of nonlinear systems has been studied in depth, such as in [11,12], but its application has so far been limited to primarily structural engineering [13][14][15][16].…”