基于各向异性的Galfenol复合悬臂梁三维非线性耦合模型

Three-dimensional Nonlinear Coupled Model of Galfenol-driven Composite Cantilever Beam Based on Anisotropy

通过Maxwell方程研究动态条件下三维驱动磁场的非线性分布,利用弱解式方程将Galfenol合金本征非线性模型与复合悬臂梁结构模型进行耦合,得到基于各向异性的悬臂梁磁机耦合非线性模型。模型仿真结果表明,磁感应强度最大的位置出现在靠近悬臂梁固定端的一侧,悬臂梁机械应变的分布结果与磁感应强度类似。分别利用非周期阶跃信号和周期正弦信号对复合悬臂梁进行试验研究。结果表明,所建立的三维非线性耦合模型可以较好地预测试验数据中的死区部分、线性区间以及饱和区间,由于柔性结构中存在的次谐波扰动,阶跃响应中试验曲线出现小幅波动现象,模型可以较好捕捉试验结果中出现的次谐波扰动特征。

The three-dimensional nonlinear distribution of the magnetic field is studied by using Maxwell equations.The nonlinear magneto-mechanical coupled model is obtained by coupling the nonlinear constitutive model of Galfenol alloy with the structural beam model.The coupled model is implemented in weak form equations.Simulations show that the maximum value of flux density shows up close to the fix end.The strain of the cantilever beam has a similar distribution as the flux density.Experimental researches are conducted by using nonperiodic step signal and periodic sinusoid signal,respectively.It is shown that the calculation results from the model are in good agreement with the experimental data.The proposed model can predict the dead zone,the linear region and the saturation region of the experimental data accurately.Also,it is shown that there are small drifts in the step response of the composite beam due to the existence of sub-harmonic disturbance.It can be seen from the model response that the proposed model can predict the drifts in step response as well.