面内平动功能梯度斜板的主动振动控制

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摘要对新型功能梯度材料制成的面内平动斜板，通过直角坐标系和斜角坐标系的坐标变换，建立了在斜角坐标系下受多个集中控制力作用的横向振动控制微分方程。采用微分求积法，将微分方程和边界条件对空间坐标进行离散化处理，得到了时域内振动控制系统的状态方程。应用最优控制法，对面内平动功能梯度斜板的无量纲运动速度小于一阶无量纲临界速度时的等幅振动和大于一阶无量纲临界速度时的发散失稳两种情况进行了数值仿真，得到控制前后若干个节点挠度随时间的变化曲线。结果表明，该方法能够有效地控制面内平动功能梯度斜板的横向振动，特别是对于发散失稳的抑制。

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	王忠民
	邹德志

关键词 ：面内平动斜板, 功能梯度材料, 最优振动控制, 微分求积法

Abstract：

Through transformation between orthogonal coordinate system and skew angle coordinate system, the transverse vibration control differential equation for in-plane translating skew plate made of a new kind of functional graded materials, subjected to multiple concentrated control forces is derived in the skew coordinate system. The differential quadrature method is used to discretize the differential equation and boundary conditions, and the state equations of the vibration control system in the time domain are set up. Using the optimal control method, the optimal control law is obtained. For the case that the axially moving velocity of in-plane translating skew plate is less than the first order dimensionless critical speed ( equilamplitude vibration) and greater than the first order dimensionless critical speed (divergence instability), some numerical simulations for the system was implemented, and variation curve between the deflection of certain point and time under uncontrolled and controlled case are plotted. The numerical results show that the optimal control scheme can effectively control the vibration of in-plane translating skew plate made of functionally graded materials, particularly for suppression of the divergence instability of skew plate.

Key words： in-plane translating skew plate functionally graded materials optimum vibration control differential quadrature method

收稿日期: 2015-03-12 出版日期: 2016-07-25

引用本文:

王忠民，邹德志. 面内平动功能梯度斜板的主动振动控制[J]. 振动与冲击, 2016, 35(15): 86-92.
WANG Zhongmin， ZOU Dezhi . Active vibration control of in-plane translating skew plate made of functionally graded materials. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(15): 86-92.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2016/V35/I15/86

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