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.

中文翻译：

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形状记忆合金振子的谐波平衡法分析

形状记忆合金（SMA）是一种非常重要的智能材料，已被广泛应用于许多领域，尤其是振动领域。相变可以通过改变温度来引起，它的刚度也相应地改变。在本文中，使用谐波平衡 (HB) 方法分析了一维 SMA 振荡器的初级共振振动。绘制了不同温度下SMA振荡器的幅频曲线，讨论了温度和频率对幅频的影响。然后，通过功率流分析（PFA）方法研究了SMA在振动过程中的能量流。分别采用解析法和数值法计算时间平均输入功率（TAIP），并比较计算时间。发现在大多数情况下解析解与数值解的差异并不显着，但解析解的计算时间仅为数值解的十分之一左右，这对于节省计算成本、实际时间控制等。最后，确定了 SMA 振荡器中能量流的一些其他特征。