Semi-analytical modeling and vibration reduction analysis of composite thin plate with MFC
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摘要:
采用压电纤维复合材料（MFC）对悬臂纤维增强复合材料薄板的振动实施主动控制，研究其半解析建模方法，并通过理论及实验对主动控制的减振效果进行了分析。在建模过程中考虑了MFC传感器/作动器对悬臂板结构系统质量矩阵和刚度矩阵的贡献，同时引入了Rayleigh阻尼和速度反馈控制提供的主动阻尼，从而使创建的半解析动力学模型能较为真实地预估MFC主动减振效果。进行了实例研究，用组建的实验系统证明了所创建的半解析模型的合理性。同时，用理论分析证明在指定的阶跃、三角形和正弦激励3种载荷作用下MFC主动控制对于复合板自由衰减振动的抑制尤为明显，进一步，用实验对主动控制的减振效果进行了量化分析，表明MFC主动控制对结构自由衰减振动的抑制可达到79.63%。最后基于所创建的半解析动力学模型分析了控制增益和MFC作动器贴敷位置对主动控制效果的影响。
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关键词:
- 压电纤维复合材料（MFC） /
- 复合材料悬臂薄板 /
- 半解析建模 /
- 主动控制 /
- 减振分析
Abstract:Piezoelectric fiber composite (MFC) was used for active vibration control of cantilevered fiber reinforced composite sheet, its semi-analytical modeling method was studied, and the damping effect of active control was analyzed through theory and experiment. In the process of modeling, the contribution of MFC sensors/actuators to the mass matrix and stiffness matrix of the cantilever plate structure system was considered, and the Rayleigh damping and active damping provided by velocity feedback control were introduced together, so that the semi-analytical dynamic model can truly predict the active vibration reduction effect of MFC. A case study was carried out, and the rationality of the semi-analytical model was proved by the established experimental system. At the same time, theoretical analysis proved that the free attenuation vibration of composite plate can be suppressed obviously by MFC active control under the specified three kinds of loads: step, triangle and sinusoidal excitation. Furthermore, the vibration reduction effect of active control was quantitatively analyzed by experiments, showing that the free attenuation vibration of composite plate can be suppressed by MFC active control by 79.63%. Finally, based on the created semi-analytical dynamic model, the effects of control gain and MFC actuator position on active control were analyzed.
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图 1 贴敷MFC复合材料悬臂薄板模型示意图
Figure 1. Schematic diagram of cantilever thin plate model of MFC composite
图 4 基于Newmark-β法计算复合结构响应的流程图
Figure 4. Flow chart of calculating the response of composite structure based on Newmark-β method
图 8 施加主动控制前后3种不同载荷激励作用下拾振点的位移响应比对
Figure 8. Comparison of displacement response of the picking point under three different loads before and after active control
图 10 实验与仿真获得的位移响应对比
Figure 10. Comparison of displacement responses obtained by experiment and simulation
图 11 不同控制增益下复合板振动响应对比
Figure 11. Comparison of vibration response of composite plates under different control gains
图 12 MFC三种不同的贴敷位置（单位：mm）
Figure 12. Three different application positions of MFC （unit: mm）
图 13 不同作动器贴敷位置复合板振动响应对比
Figure 13. Comparison of vibration response of composite plates with different actuator application positions
图 14 正弦载荷激励下MFC传感器不同贴敷位置的传感电压
Figure 14. Sensing voltage of MFC sensor at different application positions under sinusoidal load excitation
图 15 复合材料悬臂板第1阶模态应变能
Figure 15. First order modal strain energy of composite cantilever plate
表 1 T300复合材料和MFC材料参数
Table 1. T300 composite and MFC material parameters
参数 T300 MFC传感器/作动器 纤维方向弹性模量/GPa 126 30.336 横向弹性模量/GPa 8.73 15.857 切变模量/GPa 5.5 5.515 泊松比 0.31 0.31 密度/ （kg/m3） 1620 7700 介电常数/10−8 （F/m） 1.5 压电应变常数/10−12 （m/V） −171 
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表 2 理论计算与实验固有频率对比
Table 2. Comparison between theoretical calculation and experimental natural frequencies
阶次 固有频率/ Hz 误差/% 理论结果 实验结果 1 3.00 2.93 2.39 2 17.94 18.36 2.29 3 27.45 29.69 7.54 4 53.29 50.00 6.58
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表 3 主动控制实验系统仪器设备
Table 3. Instruments and equipment of active control experiment system
序号 设备名称 1 LMS 16通道便携式数据采集前端 2 LMS. Testlab笔记本工作站 3 功率放大器 4 JZK-2柔性杆激振器 5 基恩士IL-600激光位移传感器 6 电荷放大器 7 NI-9215电压输入模块 8 NI-9263电压输出模块 9 NI cDAQ-9174机箱 10 品致HA-820A高压放大器 11 LabVIEW控制端计算机 12 MFC传感器/作动器
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