Effects of supported angle on stability and dynamical bifurcations of cantilevered pipe conveying fluid

doi:10.1007/s10483-015-1946-6

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (6): 729-746.doi: https://doi.org/10.1007/s10483-015-1946-6

Effects of supported angle on stability and dynamical bifurcations of cantilevered pipe conveying fluid

Chunbiao GAN¹, Shuai JING¹, Shixi YANG¹, Hua LEI²

1. The State Key Laboratory of Fluid Power Transmission and Control, School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China;
2. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China

收稿日期:2014-06-08 修回日期:2014-10-25 出版日期:2015-06-01 发布日期:2015-06-01
通讯作者: Chunbiao GAN E-mail:cb_gan@zju.edu.cn
基金资助:
Project supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (No. 51221004), the National Natural Science Foundation of China (Nos. 11172260, 11072213, and 51375434), and the Higher School Specialized Research Fund for the Doctoral Program (No. 20110101110016)

Effects of supported angle on stability and dynamical bifurcations of cantilevered pipe conveying fluid

Chunbiao GAN¹, Shuai JING¹, Shixi YANG¹, Hua LEI²

1. The State Key Laboratory of Fluid Power Transmission and Control, School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China;
2. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China

Received:2014-06-08 Revised:2014-10-25 Online:2015-06-01 Published:2015-06-01
Contact: Chunbiao GAN E-mail:cb_gan@zju.edu.cn
Supported by:
Project supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (No. 51221004), the National Natural Science Foundation of China (Nos. 11172260, 11072213, and 51375434), and the Higher School Specialized Research Fund for the Doctoral Program (No. 20110101110016)

摘要/Abstract

摘要： The effects of the supported angle on the stability and dynamical bifurcations of an inclined cantilevered pipe conveying fluid are investigated. First, a theoretical model of the pipe is developed through the force balance and stress-strain relationship. Second, the response surfaces, stability, and critical lines of the typical hanging system (H-S) and standing system (S-S) are discussed based on the modal analysis. Last, the bifurcation diagrams of the pipe are presented for different supported angles. It is shown that pipes will undergo a series of bifurcation processes and show rich dynamic phenomena such as buckling, Hopf bifurcation, period-doubling bifurcation, chaotic motion, and divergence motion.

关键词: response characteristics, supported angle, cantilevered pipe conveying fluid, modal analysis, dynamical bifurcation

Abstract: The effects of the supported angle on the stability and dynamical bifurcations of an inclined cantilevered pipe conveying fluid are investigated. First, a theoretical model of the pipe is developed through the force balance and stress-strain relationship. Second, the response surfaces, stability, and critical lines of the typical hanging system (H-S) and standing system (S-S) are discussed based on the modal analysis. Last, the bifurcation diagrams of the pipe are presented for different supported angles. It is shown that pipes will undergo a series of bifurcation processes and show rich dynamic phenomena such as buckling, Hopf bifurcation, period-doubling bifurcation, chaotic motion, and divergence motion.

Key words: supported angle, response characteristics, cantilevered pipe conveying fluid, modal analysis, dynamical bifurcation

中图分类号:

TH113

Chunbiao GAN, Shuai JING, Shixi YANG, Hua LEI. Effects of supported angle on stability and dynamical bifurcations of cantilevered pipe conveying fluid[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(6): 729-746.

参考文献

[1] Zhang, Y. L., Gorman, D. G., and Reese, J. M. Vibration of prestressed thin cylindrical shells conveying fluid. Thin-Walled Structures, 41, 1103-1127 (2003)
[2] Päidoussis, M. P., Price, S. J., and de Langre, E. Fluid-Structure Interactions: Cross-Flow-Induced Instabilities, Cambridge University Press, Cambridge (2010)
[3] Ashley, H. and Haviland, G. Bending vibrations of a pipe line containing flowing fluid. Journal of Applied Mechanics-Transactions of the ASME, 17, 229-232 (1950)
[4] Housner, G. W. Bending vibrations of a pipe line containing flowing fluid. Journal of Applied Mechanics-Transactions of the ASME, 19, 205-208 (1952)
[5] Benjamin, T. B. Dynamics of a system of articulated pipes conveying fluid-parts, I: theory. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 261, 457-486 (1961)
[6] Benjamin, T. B. Dynamics of a system of articulated pipes conveying fluid, II: experiments. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 261, 487-499 (1961)
[7] Gregory, R. W. and Päidoussis, M. P. Unstable oscillation of tubular cantilevers conveying fluid, I: theory. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 293, 512-527 (1966)
[8] Gregory, R. W. and Päidoussis, M. P. Unstable oscillation of tubular cantilevers conveying fluid, II: experiments. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 293, 528-545 (1966)
[9] Firouz-Abadi, R. D., Askarian, A. R., and Kheiri, M. Bending-torsional flutter of a cantilevered pipe conveying fluid with an inclined terminal nozzle. Journal of Sound and Vibration, 332, 3002-3014 (2013)
[10] Päidoussis, M. P., Li, G. X., and Moon, F. C. Chaotic oscillations of the autonomous system of a constrained pipe conveying fluid. Journal of Sound and Vibration, 135, 1-19 (1989)
[11] Li, G. X. and Päidoussis, M. P. Stability, double degeneracy and chaos in cantilevered pipes conveying fluid. International Journal of Non-Linear Mechanics, 29, 83-107 (1994)
[12] Jin, J. D. Stability and chaotic motions of a restrained pipe conveying fluid. Journal of Sound and Vibration, 208, 427-439 (1997)
[13] Wadham-Gagnon, M., Päidoussis, M. P., and Semler, C. Dynamics of cantilevered pipes conveying fluid, part 1: nonlinear equations of three-dimensional motion. Journal of Fluids and Structures, 23(4), 545-567 (2007)
[14] Modarres-Sadeghi, Y., Semler, C., and Wadham-Gagnon, M. Dynamics of cantilevered pipes conveying fluid, part 3: three-dimensional dynamics in the presence of an end-mass. Journal of Fluids and Structures, 23, 589-603 (2007)
[15] Modarres-Sadeghi, Y. and Päidoussis, M. P. Chaotic oscillations of long pipes conveying fluid in the presence of a large end-mass. Computers and Structures, 122, 192-201 (2013)
[16] Päidoussis, M. P. and Semler, C. Non-linear dynamics of a fluid-conveying cantilevered pipe with a small mass attached at the free end. International Journal of Non-Linear Mechanics, 33, 15-32 (1998)
[17] Bajaj, A. K. and Sethna, P. R. Effect of symmetry-breaking perturbations on flow-induced oscillations in tubes. Journal of Fluids and Structures, 5, 651-679 (1991)
[18] Wang, Z. L., Feng, Z. Y., Zhao, F. Q., and Liu, H. Z. Analysis of coupled-mode flutter of pipes conveying fluid on the elastic foundation. Applied Mathematics and Mechanics, 21, 1177-1186 (2010)
[19] Wang, L. Flutter instability of supported pipes conveying fluid subjected to distributed follower forces. Acta Mechanica Solida Sinica, 25, 46-52 (2012)
[20] Päidoussis, M. P. and Li, G. X. Pipes conveying fluid: a model dynamical problem. Journal of Fluids and Structures, 7, 137-204 (1993)
[21] Päidoussis, M. P. Fluid-Structure Interactions, Academic Press, Pittsburgh (2003)
[22] Päidoussis, M. P. Dynamics of tubular cantilevers conveying fluid. Journal of Mechanical Engineering Science, 12, 85-103 (1970)
[23] Wang, L. and Ni, Q. A note on the stability and chaotic motions of a restrained pipe conveying fluid. Journal of Sound and Vibration, 296, 1079-1083 (2006)
[24] Panda, L. N. and Kar, R. C. Nonlinear dynamics of a pipe conveying pulsating fluid with combination, principal parametric and internal resonances. Journal of Sound and Vibration, 309, 375-406 (2008)
[25] Zhang, Y. L. and Chen, L. Q. External and internal resonances of the pipe conveying fluid in the supercritical regime. Journal of Sound and Vibration, 332, 2318-2337 (2013)
[26] Nayfeh, A. H. and Balachandran, B. Modal interactions in dynamical and structural systems. Applied Mechanics Review, 42, 175-201 (1989)
[27] Päidoussis, M. P. and Moon, F. C. Nonlinear and chaotic fluid-elastic vibrations of a flexible pipe conveying fluid. Journal of Fluids and Structures, 2, 567-591 (1988)
[28] Qian, Q., Wang, L., and Ni, Q. Nonlinear responses of a fluid-conveying pipe embedded in nonlinear elastic foundations. Acta Mechanica Solida Sinica, 21, 170-176 (2008)
[29] Liang, F. and Wen, B. C. Forced vibrations with internal resonance of a pipe conveying fluid under external periodic excitation. Acta Mechanica Solida Sinica, 24, 477-483 (2011)

Effects of supported angle on stability and dynamical bifurcations of cantilevered pipe conveying fluid

Effects of supported angle on stability and dynamical bifurcations of cantilevered pipe conveying fluid

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