压电纤维复合材料对悬臂结构的作动行为研究
RESEARCH ON ACTION BEHAVIOR OF MACRO FIBER COMPOSITES APPLIED IN CANTILEVER STRUCTURES
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摘要: 压电纤维复合材料(macro fiber composite, MFC)是由美国NASA研发的综合性能优秀的新型压电材料, 掌握MFC的力学行为有利于将其投入结构变形控制、减振降噪和健康监测等领域. 目前对MFC宏观力学行为的研究中缺乏对作动力与驱动电压直接关系的研究, 现有的以MFC为作动器的应用中所使用力电关系的精度有限, 不利于将MFC投入更精密的使用场景. 针对此问题, 文章采用经典板理论, 考虑了MFC与受控结构的相对尺寸, 推导了MFC对悬臂结构的作动力方程. 为兼顾计算的准确性和便利性, 建立了考虑MFC叉指电极真实电场的精细有限元模型开展压电静力仿真, 给出将MFC叉指电极的弯曲电场简化为匀强电场的修正系数. 搭建MFC-悬臂梁结构的实验装置, 对有限元模型和作动力公式加以验证. 精细模型与简化模型的仿真结果与实验进行对比, 总体误差较小, 验证了模型和修正系数的可靠性. 理论计算与仿真结果对比, 误差在1%以内, 表明所得作动力预测公式在较大的宽度比范围内均具有较好精度. 建立的MFC作动力模型对MFC应用于悬臂结构的变形控制和振动抑制有一定指导意义.Abstract: Macro fiber composite (MFC) is a new kind of piezoelectric material with excellent performances developed by NASA Langley Research Center. An accurate understanding of the mechanical behavior of MFC helps to apply it to structural deformation control, vibration control, noise reduction, health monitoring and other fields. However, there are few researches on the macroscopic mechanical behavior of MFC in the literature, especially about the relationship between the actuating force and the voltage. The limited accuracy of the relationship between the actuating force and the voltage is not conducive to apply MFC to more precise application scenarios. In the present paper, the actuation equation of MFC acting on a cantilever structure is derived by considering the relative dimensions of MFC and the controlled structure to overcome this problem based on classic plate theory. For sake of the balance of the accuracy and convenience for the simulation, a detailed finite element model considering the bending electric field of the interdigitated electrode of MFC is established to carry out piezoelectric-static simulation. A correction coefficient is introduced for simplifying the electric field of the interdigitated electrode. A piezoelectric-static experiment is carried out to validate the finite element model and the actuation formula for a MFC-cantilever beam. The simulation results of the detailed model and the simplified model are compared with the experiment. The relative error between the simulations and the experiment is little, which verifies the reliability of the model and the correction coefficient of the curved electric field. The correctness of the theoretical analysis is verified by the simulation results, which indicates the actuation prediction formula has a good precision in a wide range of width ratio between MFC and the controlled structure. The actuating model of MFC established in this paper has a certain guiding significance for the application of MFC to the deformation control and vibration suppression for cantilever structures.