压电纤维材料驱动下复合板扭曲变形效率分析
Efficiency of twist deformation of composite plate actuated by MFC

摘要 含有主动材料的复合结构越来越多地应用于自适应结构中。主动纤维材料的应用为复合结构带来了新的特性也使其设计更为复杂。针对受压电纤维材料（MFC）驱动的主动材料复合板的变形进行研究，目的在于获得MFC驱动复合板扭曲变形与MFC纤维铺设及驱动模式的关系。基于弹性力学理论建立了受电压作用主动纤维产生的应变与由此导致的复合板的内力、变形之间的关系，并利用Ritz法，通过假设双向梁函数组合级数的位移场建立了该问题的求解方法，经推导得到了MFC驱动下位移场的求解方程，实验结果验证了其有效性。为了评估MFC驱动复合板在不同条件下的驱动效果，针对复合板变形所具有的弯扭耦合特点，在定义复合板截面等效扭转角和等效弯曲角的基础上提出了主动复合板驱动扭曲变形效率的概念和计算方法，利用该方法分析了MFC的铺设角度以及电压驱动模式对复合板扭曲变形效率的影响。依据分析所得到的结果给出了对应不同约束条件的MFC驱动复合板主动纤维布置及驱动模式的选择方案。
Abstract：More and more composite structures containing active materials are applied to adaptive structures. The integration of active materials in structures has brought new characteristics but made the design more complicated. In this paper, the deformation of the active composite plate actuated by the macro fiber material (MFC) is studied. The purpose is to obtain the relationship between the twist deformation of the actuated composite plate and the MFC fiber laying and the actuation mode. Based on the elastic mechanics theory, the relationship between the strain of active fiber actuated by voltage and induced internal force and deformation of the composite plate is established. The solution of the problem is conducted using Ritz's method and taking the displacement function as a linear combination of the two-dimension beam-modes. The solving equation of the displacement field actuated by MFC is derived, and the analytical result is verified by the experiment. In order to evaluate the actuation effect of MFC composite plate under different conditions and to consider the bending-torsion coupling characteristics of composite plate deformation, the concept and the calculation of actuation efficiency of an active composite plate are proposed, which is based on the definition of equivalent bending and twist angle of section. Then the evolution of the actuation efficiency with the laying angle of MFC and the mode of input voltage is analyzed. Corresponding to different constraint conditions, the laying of piezoelectric fiber-direction and the selection of actuation-mode are given based on the obtained analysis results.