柔性空间结构高阶有限元模型与主动振动控制研究

Research on High Order Finite Element Model and Active Vibration Control for Flexible Space Structures

应用压电材料实现大型柔性空间结构的振动控制引起了广泛关注。针对上下表面粘贴压电层的复合层梁结构,采用高阶位移场模型,利用线性热压电本构关系和Hamilton原理导出了层梁结构的高阶有限元模型。电势和温度沿厚度方向的分布均采用线性模型。采用常增益速度负反馈控制、Lyapunov反馈控制和基于独立模态的线性二次型调节器(LQR)设计主动控制器,实现了层梁结构脉冲激励和热载荷作用下的振动主动控制。仿真结果表明,LQR方法更能有效的实现结构振动控制,其振动衰减时间较短,作动器峰值电压更低,但不能消除热载荷引起的结构静变形。

Vibration control using piezoelectric materials for large flexible space structures had attracted significant attention. In this paper, the high order finite element formulation of sandwich beam bonded piezoelectric layers was developed through the linear thermopiezoelectric consitutive relations and Hamilton principle. The mathematical model was based on a high order dis- placement field coupledwith a linear electric potential and temperature field. The constant-gain negative velocity feedback, Lyapunov feedback as well as a linear quadratic regulator（LQR） approach had been used for active vibration control with the beam subjected to impact excitations and/or thermal loads. The LQR approach is found to be more effective in vibration control with lesser time for vibration suppressed, and lesser peak voltages applied in the piezo actuator, however the thermal induced offset is not controlled using the LQR scheme.