Analysis of shape memory alloy vibrator using harmonic balance method
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Analysis of shape memory alloy vibrator using harmonic balance method Haoyuan Du1 · Xuan He1 · Linxiang Wang1 · Roderick Melnik2 Received: 9 April 2020 / Accepted: 19 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Shape memory alloy (SMA) is a very important smart material, which has been widely used in many fields, especially in vibration. Phase transformation can be induced by changing temperature and its stiffness changes accordingly. In this paper, the primary resonance vibration of a one-dimensional SMA oscillator is analyzed using the harmonic balance (HB) method. The amplitude-frequency curves of the SMA oscillator with different temperatures are drawn, and the effect of temperature and frequency on the amplitude is discussed. Then, the energy flow of SMA in the vibration process is researched by the power flow analysis (PFA) approach. The time-averaged input power (TAIP) is calculated using the analytical and numerical method, respectively, and the calculation time is compared. It is found that the difference between the analytical and numerical solutions is not significant in most cases, but the calculation time of analytical solution is only about one-tenth of that of the numerical solution, which is very important in saving computational cost, real-time control and so on. Finally, some other characteristics of energy flow in the SMA oscillator are identified. Keywords Shape memory alloy · Analytical solution · Amplitude–frequency characteristics · Power flow analysis
1 Introduction Due to the important and unique thermo-mechanical properties, shape memory alloys (SMA) are widely known and used. It can convert thermal energy into mechanical energy directly, and vice versa [1], which makes it very attractive in many engineering applications, such as mechanical engineering, biomedicine, robotics and so on [2–8]. Among the applications mentioned above, SMA vibration damper may be the most common one [1, 9]. When the temperature changes, the phase transformation between the martensite phase (at low temperature) and the austenite phase (at high temperature) can be induced in SMA materials [10–12]. And at low temperatures, SMA material can be switched between multiple martensitic variants by external loading [13]. These phenomena can be explained by the theory of * Linxiang Wang [email protected] 1
State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, 310027 Hangzhou, People’s Republic of China
MS2Dicovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON N2L 3L5, Canada
2
Landau theory of phase transition, and the potential energy of a typical SMA with different temperatures is plotted as Fig. 1 [10, 13]. As shown in Fig. 1, when the temperature is relatively low, as curve a, there are only two local minima in the potential energy diagram of SMA, which represents the twin martensite phase with different orientations. When no external load is applied, only the two martensite phases are stable due to the m
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