Analysis of shape memory alloy vibrator using harmonic balance method

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.