复合材料层合板的颤振特性及振动抑制研究

研究了超声速流中压电复合材料层合板的颤振特性及振动抑制方法。采用一阶活塞理论计算了超声速流场中的气动压力，基于经典层合板理论和Hamilton原理推导了压电复合材料层合板的动力学模型，设计了滑模观测器以减少观测溢出，通过Lyapunov方法证明观测器的稳定性，应用观测状态设计了LQR控制器，讨论了几何参数、铺设角度对压电复合材料层合板颤振特性的影响，利用SIMULINK仿真求解了层合板的脉冲响应，验证了控制器的有效性。结果表明，合理规划层合板的几何参数和铺设角度可提高系统颤振稳定性，滑模观测器能够较为准确地追踪原始系统且具有良好的鲁棒性，LQR控制可以在一定范围内消除层合板的颤振点，并且能够有效地控制压电复合材料层合板在颤振边界处的振动，Q矩阵越大，振动控制效果越好，压电层厚度越大，LQR控制效果越好。

Study on Flutter Characteristics and Vibration Suppression of a Composite Laminated Plate

The flutter characteristics and the vibration suppression of a composite laminate in the supersonic flow are studied. The first-order piston theory is used to calculate the aerodynamic pressure in the supersonic flow field. The dynamic model of a piezoelectric composite laminate is deduced by using the classical laminate theory and the Hamilton's principle. The sliding observer is designed to reduce the observation overflow, and the Lyapunov method is used to prove the stability. The LQR controller is designed based on the observed state. The effects of geometric parameters and fiber angles on the flutter characteristics of piezoelectric composite laminates are studied. The impulse response of the laminated plate is solved by SIMULINK simulation to verify the effectiveness of the controller. The results show that reasonable planning of the geometric parameters and fiber angle of the laminated plate can improve the system flutter stability. The sliding mode observer can trace the original system more accurately and has good robustness. The LQR control can eliminate the flutter point of the laminate within a certain range, and also can effectively suppress the vibration of the piezoelectric composite laminate at the flutter boundary, with the increase of the Q matrix, and the vibration suppression effect is better. The LQR control effect is better with the thickness of the piezoelectric layer becomes larger.