磁致伸缩层合悬臂梁式作动器的振动分析

为了分析磁致伸缩薄膜型层合悬臂梁式作动器的振动问题，应用磁致伸缩材料的非线性本构关系，由哈密尔顿原理导出了双层悬臂梁的振动微分方程。采用分离变量方法和常微分方程组的解析解法对磁致伸缩薄膜型层合悬臂梁的自由振动和受迫振动进行了理论分析。数值算例表明本文计算结果与有限元结果吻合较好，从而佐证了本文理论模型和求解方法的正确性，并讨论了几何参数、材料参数对层合梁固有频率的影响。还分析了在周期输入磁场激励下悬臂梁的挠度响应，且挠度响应呈现出倍频效应的动态特性。 

Vibration analysis of magnetostrictive laminated cantilever actuator

Differential equation to analyze the vibration problem of a magnetostrictive laminated cantilever with thin-film actuator was derived by Hamilton's variational principle, using the nonlinear constitutive relation of magnetostrictive material. The free vibration and forced vibration of magnetostrictive laminated cantilever with thin-film were analyzed by means of the methods of separation variables and the analytic solution of ordinary differential equations. The numerical example shows that the calculation results of this paper are in good agreement with finite element results, which evidences validity of the theoretical model and solution method, and the effect of the geometric parameters and material parameters on natural frequency of the laminated beam was discussed. The deflection response of beam excited by a periodic input magnetic field was also analyzed, which present the dynamic characteristic of frequency multiplying effect. The deflection response of the cantilever beam excited by a periodic input magnetic field was also analyzed, which presented the double frequency effect of dynamic characteristics.