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

PDF(1343 KB)

Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (4) : 182-187.

WANG Zhong-Min, ZOU De-Zhi， JIANG Quan-You

Author information +

History +

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.

Key words

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

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

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

References

[1] 王忠民, 冯振宇, 赵凤群, 刘宏昭. 弹性地基输流管道的耦合模态颤振分析[J]. 应用数学和力学, 2000, 21(10): 1060-1068.
WANG Zhong-min, FENG Zhen-yu, ZHAO Feng-qun, LIU Hong-zhao. Analysis of coupled mode flutter of pipes fluid on the elastic foundation[J]. Applied Mathematics and Mechanics, 2000, 21 (10): 1060-1068.
[2] 王忠民, 张战午, 李会侠. 粘弹性地基上粘弹性输流管道的稳定性分析[J]. 计算力学学报, 2005, 22(5): 613- 617.
WANG Zhong-min, ZHANG Zhan-wu, LI Hui-xia. Stability analyses of viscoelastic pipes conveying fluid on viscoelastic foundation[J]. Chinese Journal of Compu- tational Mechanics, 2005, 22(5): 613-617.
[3] 王忠民, 张战午, 李会侠. 弹性地基上输送振荡流粘弹性管道的动力稳定性[J]. 机械工程学报, 2005, 41 (10): 57-60.
WANG Zhong-min, ZHANG Zhan-wu, LI Hui-xia. Dynamic stability of viscoelastic pipes conveying pulsating fluid on the elastic foundation[J]. Chinese Journal of Mechanical Engineering, 2005, 41(10): 57-60.
[4] Vassilev Vassil M，Djondjorov Peter A. Dynamic stability of viscoelastic pipes on elastic foundations of variable modulus[J]. Journal of Sound and Vibration, 2006, 297(3): 414-419.
[5] 包日东, 闻邦椿. 分析弹性支承输流管道的失稳临界流速[J]. 力学与实践, 2007, 29(4): 24-28.
BAO Ri-dong, WEN Bang-chun. Analysis of critical instability flowrate of pipeline conveying fluid with elastic supports[J]. Mechanics in Engineering, 2007, 29(4): 24-28.
[6] 梁峰, 金基铎, 杨晓东, 闻邦椿. 弹性地基上输流管道的静态和动态稳定性研究[J]. 工程力学, 2010, 27(11): 166-171.
LIANG Feng, JIN Ji-duo, YANG Xiao-dong，WEN Bang- chun. Static and dynamic stabilities of fluid pipes on elastic foundation[J]. Engineering Mechanics, 2010, 27(11): 166-171.
[7] 梁峰，金基铎，李伟杰，闻邦椿. Winkler地基上输流管道的临界流速分析[J]. 机械强度, 2011, 33(1): 20- 23.
LIANG Feng, LI Wei-jie, YANG Xiao-dong, WEN Bang-chun. Critical velocity of pipes conveying fluid resting on Winkler foundation[J]. Journal of Mechanical Strength, 2011, 33(1): 20-23.
[8] 邹光胜，金基铎，闻邦椿. 受约束悬臂输流管振动的最优控制[J]. 东北大学学报, 2003, 25 (3): 277-279.
ZOU Guang-sheng, JIN Ji-duo, WEN Bang-chun. Optimal control of vibration in restrained cantilever piping for fluid delivery[J]. Journal of Northeastern University (Natural Science), 2003, 25 (3): 277-279.
[9] 张锴锋. 两端固定脉动流管道振动的白适应控制[J]. 机械设计与制造, 2008, No.12: 149-151.
ZHANG Kai-fen. Adaptive control of vibration of a clamped-clamped pipe conveying pulsating fluid[J]. Machinery Design & Manufacture, 2003, 25 (3): 277-279.
[10] 梁峰. 输流管道横向振动机理及其控制研究[D]. 沈阳：东北大学，2009.
LIANG Feng. Study on the mechanism of transverse vibration and its control of pipes conveying fluid[J]. Shenyang: Northeastern University, 2009.
[11] 梁建术, 王涛, 李欣业. 基于Ansys的输液管道系统的振动控制分析[J]. 机械强度，2012, 34 (4): 486-490.
LIANG Jian-shu, WANG Tao, LI Xin-ye. Vibration control analysis of liquid conveying pipe system based on Ansys[J]. Journal of Mechanical Strength, 2012, 34 (4): 486-490.
[12] Lin Y H, Chu C L. Comments on “Active model control of vortex-induced vibrations of a flexible cylinder”[J]. Journal of Sound and Vibration, 1994, 175(1): 135-137.
[13] 严宗达著. 结构力学中的富里叶级数解法[M]. 天津: 天津大学出版社, 1989.
[14] 王鑫伟. 微分求积法在结构力学中的应用[J]. 力学进展, 1995, 25(2): 232-240.
WANG Xin-wei. Differential quadrature in the analysis of structural components[J]. Advances in Mechanics. 1995, 25(2): 232-240.
[15] 顾仲权, 马扣根, 陈卫东编著. 振动主动控制[M]. 北京：国防工业出版社，1997.