SMA纤维混杂复合材料箱型薄壁悬臂梁的固有频率

Natural frequencies of thin-walled composite cantilever box beams with SMA fibers

研究SMA纤维驱动下的复合材料箱型薄壁悬臂梁的固有振动频率特性。根据SMA主动纤维复合材料箱型悬臂梁的横截面二维分析模型,采用Hamilton原理导出具有拉伸-扭转-弯曲变形耦合的梁的自由振动偏微分方程组。由上述一般的弹性耦合振动方程出发,讨论周向均匀刚度配置以及周向反对称刚度配置等特殊情形,并且给出拉伸-扭转耦合、弯曲-扭转耦合固有振动频率的精确解。通过数值计算,分析了SMA纤维在激活状态下对复合材料箱型薄壁悬臂梁固有频率的影响机理。

The natural vibration behavior of thin-walled composite cantilever beams with SMA fiber actuation was studied.The coupled equations of free vibration of active anisotropic thin-walled box-beams incorporating SMA fibers were derived using the active two-dimensional analysis model developed based on Hamilton's variational principle.The general form of coupled equations of motion was applied to the cases of circumferentially uniform(CUS) and circumferentially antisymmetric(CAS) fiber installation.Closed form expressions for natural frequencies,corresponding respectively to the extension-twist coupling vibration and bending-twist coupling vibration were provided.Numerical studies were presented to compare the proposed model with the previously established passive model.The effects of SMA actuation and elastic coupling on frequencies were evaluated.