弹性地基上输流管道主参数共振的主动振动控制

王忠民, 邹德志, 姜全友

振动与冲击 ›› 2016, Vol. 35 ›› Issue (4) : 182-187.

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振动与冲击 ›› 2016, Vol. 35 ›› Issue (4) : 182-187.
论文

弹性地基上输流管道主参数共振的主动振动控制

  • 王忠民, 邹德志, 姜全友
作者信息 +

Active vibration control for principal parametric resonance of pipes conveying fluid resting on elastic foundations

  • WANG Zhong-Min,  ZOU De-Zhi,  JIANG Quan-You
Author information +
文章历史 +

摘要

研究了弹性地基上输送脉动流管道主参数共振的主动振动控制问题。在管道上、下两侧对称的粘贴一对陶瓷压电片,利用压电效应使压电片对管道施加控制力矩。对运动微分方程中由控制力矩产生的Dirac Delta函数对轴向坐标的一阶导数,利用Fourier级数进行展开,再采用微分求积法对控制微分方程和边界条件进行离散化处理,得到了时变系统的状态方程。以管道的横向振动变形和输入控制能量之和达到最小的最优控制原则,对简支输流脉动流管道的时变系统受控前后某些点的挠度响应进行了数值仿真。数值计算结果表明,采用的最优控制方案能有效地控制输送脉动流管道的主参数共振问题。

Abstract

This paper investigates active vibration control for principal parameter resonance of pipe conveying pulsating flow resting on elastic foundation. Using piezoelectric effect of piezoelectric materials, a pair of piezoelectric ceramic patches is pasted symmetrically on above and below the pipe to apply control moment to the pipe. The first derivative of Dirac Delta function with respect to the axial coordinate resulting from a control moment term of the differential equations of motion is expanded to a Fourier series. Employing the differential quadrature method, the differential equation of motion and boundary condition of the pipe are discretized, and then the state equations with the time-varying system are derived. The criterion of optimal control is that the sum of transverse vibration energy of the pipe conveying fluid and the input control energy can be minimized simultaneously. The numerical simulations for certain deflection responses of simply supported pipe conveying pulsating fluid are implemented under uncontrolled and controlled case. The numerical results show that the optimal control scheme can effectively control the primary parametric resonance of pipe conveying pulsating flow. 

关键词

输送脉动流管道 / 弹性地基 / 微分求积法 / 最优控制法 / 压电效应

Key words

pipes conveying pulsating fluid / elastic foundation / differential quadrature method / optimal control method / piezoelectric effect

引用本文

导出引用
王忠民, 邹德志, 姜全友. 弹性地基上输流管道主参数共振的主动振动控制[J]. 振动与冲击, 2016, 35(4): 182-187
WANG Zhong-Min, ZOU De-Zhi, JIANG Quan-You. Active vibration control for principal parametric resonance of pipes conveying fluid resting on elastic foundations[J]. Journal of Vibration and Shock, 2016, 35(4): 182-187

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