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该文采用摄动解法研究了磁致伸缩作动器中的关键结构元件Terfenol-D杆在初值条件下的振动问题。杆的初始状态是静止的,其振动是由交变电流激励而产生的。由于采用了标准平方型本构关系,这使得问题的基本方程及边界条件都是时间变系数的。考虑到问题的数学模型中含有小参数,周期交变电流激励下的位移响应的近似解析解可以用摄动解法得到。计算结果表明在低频电流下位移响应是周期的,并显示出倍频特征。最后还分析了材料的磁致伸缩常数及电流参数对输出位移的影响。
In this paper, the perturbation solution method is used to study the vibration of Terfenol-D rod, a key structural element in a magnetostrictive actuator, under initial conditions. The initial state of the rod is stationary, the vibration is generated by the alternating current excitation. As a result of the standard squared type constitutive relations, which makes the problem of the basic equations and boundary conditions are time-varying coefficients. Considering that the mathematical model of the problem contains small parameters, the approximate analytical solution of the displacement response under cyclic alternating current excitation can be obtained by the perturbation solution method. The calculated results show that the displacement response is periodic under low frequency current and shows frequency doubling characteristics. Finally, the effect of magnetostrictive constant and current parameter of the material on the output displacement is also analyzed.