An Active Control Method for Chaotic Motion of Fluid Conveying Pipe under Harmonic Excitation of Supports

Abstract:

The chaotic motion of a single mode system of the fixed supported pipe at two ends under the base excitation was actively controlled by introducing the feedback of notch filter. The equations of both homoclinic and periodic orbits of the unperturbed system were derived firstly, and then the corresponding Melnikov functions were deduced. Based on the conditions that the Melnikov functions corresponding to the homoclinic and periodic orbits respectively had themselves simple zeros, the conditions that parameters should satisfy to introduce the chaotic motion of the system into periodic orbits could be obtained. Lastly, numerical simulation was used for the response of the perturbed system, and the simulation results showed that the system’s chaotic motion can be successfully induced to periodic motion. For different feedback gains of the notch filter, the responses of the system would converge on different stable periodic solutions.

• Periodical: Applied Mechanics and Materials (Volume 120)
• Pages: 537-546
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.120.537
• Online since: October 2011
• Authors: Ri Dong Bao
• Keywords: Base Excitation, Chaotic Motion, Feedback Control, Fluid Conveying Pipe, Notch Filter

References

[1] M P Paidoussis, G X Li. Journal of Fluid and Structures, 1993, 7:137-204.

[2] H Doki, J Tani. Transactions of JSME Series C, 1988, 54: 357-362.

[3] H Doki, K Aso, K Kanno. Transactions of JSME Series C, 1995, 61:1816-1821.

[4] H Doki et al. Transactions of JSME Series C, 1996, 62:3394-3399.

[5] H Doki, K Hiramoto, R E Skelton. Journal of Fluids and Structures, 1998,12:615-628.

[6] C H Ya, A K Bajaj, O D Nwokaih. Journal of Fluids and Structures, 1995,9:99-122.

[7] S E Semercigil, Ö F Turan, S Lu. Journal of Sound and Vibration,1997,205(1):103-111.

[8] J Tani, Y Sudani. JSME International Journal, Series C, 1995,38(1):55-58.

[9] Y H Lin, C L Chu. Journal of Sound and Vibration, 1996, 196(1):97-105.

[10] Y H Lin, Y K Tsai. International Journal of Solids Structures, 1997,34(23): 2945-2956.

[11] Y H Lin, Y K Tsai. Journal of Sound and Vibration, 1997,202(4):477-490.

[12] Ridong Bao, Bangchun Wen. Journal of Northeastern University (Natural Science), 2007, 28(7): 1017-1020. (In Chinese)

[13] C Semler, G X Li, M P Paidoussis. Journal of Sound and Vibration, 1994,169(5):577-599.

[14] Jiduo Jin, Guangsheng Zou, Bangchu Wen. Chinese Journal of Applied Mechanics, 2005, 22(1): 111－113. (In Chinese)

[15] Chaohong Cai, Zhenyuan Xu, Wenbo Xu. ACTA Physica Sinaca, 2001, 50(10): 1846-1850. (In Chinese)

[16] W J Grantham, A M Athalye. Notch filter control for k-period motion in a chaotic system // Boston: Birkhouser, 1997.

DOI: 10.1007/978-1-4612-2446-4_9

[17] Zengrong Liu. Chaotic Perturbation Criterion [M]. Shanghai: Shanghai Science and Technology Press, 1994. (In Chinese)

[18] B D Greenspan, P J Holmes. Siam. J. Math. Aral,1984, 15(1): 69-97.