Research on impact vibration response of a simply supported fluid conveying pipe excited by pulsating internal flow under unilateral constraint

PDF(2803 KB)

Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (22) : 210-219.

WANG Tianlin1,GUO Changqing2,QI Fahui1,XU Feng2,LU Xiaomian3,FANG Mengmeng4

Author information +

History +

Abstract

By using a nonlinear spring with infinitesimal stiffness in tension but rapidly increasing stiffness in compression to simulate the unilateral constraint, the nonlinear dynamic behaviors of a simply supported fluid conveying pipe with a unilateral constraint under the excitation of pulsating internal flow under are studied. The influences of pulsating excitation frequency, parameters such as flow velocity, axial coordinate and lateral spacing of the constraint on the dynamic characteristics of the pipe are analyzed. There are three main paths from stable periodic motion to chaos in simply supported pipe under unilateral constraints: almost periodic motion leads to chaos window, period-doubling bifurcation leads to chaos window, and directly leads to chaos window. The characteristic phenomena of the non-smooth vibration system, such as N2/N1 periodic impact vibration, period-doubling of impact response and grazing motion have been observed. The proper position of the unilateral constraint can greatly reduce the maximum response amplitude of fluid conveying pipe, and even make fluid conveying pipe and the constraint is always in a sticky state.

Key words

fluid conveying pipe / unilateral constraint / pulsating internal flow excitation / impact vibration / chaotic

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

WANG Tianlin1,GUO Changqing2,QI Fahui1,XU Feng2,LU Xiaomian3,FANG Mengmeng4. Research on impact vibration response of a simply supported fluid conveying pipe excited by pulsating internal flow under unilateral constraint[J]. Journal of Vibration and Shock, 2023, 42(22): 210-219

References

[1] Heng J, New T H, Wilson P A. Application of an Eulerian granular numerical model to an industrial scale pneumatic conveying pipeline [J]. Advanced Powder Technology, 2018, 30(2): 240-256.
[2] Wang F S, Wei Z, Li P, et al. Initial crack propagation and the influence factors of aircraft pipe pressure [J]. Materials, 2019, 12(19): 3098-3098.
[3] Shen T, Park S, Du J K, et al. A further study on fracture resistance evaluation of nuclear pipes using CP specimens [J]. Engineering Fracture Mechanics, 2020, 235(prepublish).
[4] 尹渊博，袁辰，杜荟敏，等. 基于扰动响应的输油管道泄漏检测方法[J]. 振动与冲击, 2022, 41(23): 43-50.
YIN Yuan-bo, YUAN Chen, DU Hui-min, et al. Leakage detection method of oil pipeline based on disturbance response [J]. Journal of Vibration and Shock , 2022, 41(23): 43-50.
[5] Zheng T, Liang Z, Zhang L, et al. Safety assessment of buried natural gas pipelines with corrosion defects under the ground settlement [J]. Engineering Failure Analysis, 2021, 129.
[6] Javadi M, Noorian M A, Irani S. Stability analysis of pipes conveying fluid with fractional viscoelastic model [J]. Meccanica, 2019, 54(3): 399-410.
[7] Elnajjar J, Daneshmand F. Stability of horizontal and vertical pipes conveying fluid under the effects of additional point masses and springs [J]. Ocean Engineering, 2020, 206(c).
[8] 张挺，林震寰，林通，等. 内激励型振荡衰减流作用下输流管道动力不稳定分析[J]. 振动与冲击, 2021, 40(3): 284-290.
ZHANG Ting, LIN Zhen-huan, LIN Tong, et al. Dynamic instability analysis of pipeline conveying fluid under action of
internally excited oscillation attenuation flow [J]. Journal of Vibration and Shock , 2022, 40(3): 284-290.
[9] Duan N, Lin S D, Wu Y H, et al. Stability analysis of a pipe conveying fluid with a nonlinear energy sink [J]. Science China (Information Sciences), 2021, 64(5).
[10] Paidoussis M P, Li G X, Moon F C. Chaotic oscillations of the autonomous system of a constrained pipe conveying fluid [J]. Journal of Sound and Vibration, 1989, 135(1): 1-19.
[11] Paidoussis M P, Li G X, Rand R H. Chaotic motions of a constrained pipe conveying fluid: comparison between simulation, analysis and experiment [J]. Journal of Applied Mechanics, 1991, 58(2): 559-565.
[12] Paidoussis M P, Semler C. Nonlinear and chaotic oscillations of a constrained cantilevered pipe conveying fluid: A full nonlinear analysis [J]. Nonlinear Dynamics, 1993, 4(6): 655-670.
[13] Wang L, Ni Q. A note on the stability and chaotic motions of a restrained pipe conveying fluid [J]. Journal of Sound and Vibration, 2006, 296(4): 1079-1083.
[14] Jin J D. Stability and chaotic motions of a restrained pipe conveying fluid [J]. Journal of Sound and Vibration, 1997, 208(3): 427-439.
[15] 唐冶，方勃，张业伟，等. 非线性弹簧支承悬臂输液管道的分岔与混沌分析[J]. 振动与冲击，2011, 30(8): 269-274.
TANG Ye, FANG Bo, ZHANG Ye-wei, et al. Bifurcation and chaos analysis of cantilever pipeline conveying fluid with nonlinear spring support [J]. Journal of Vibration and Shock, 2011, 30(8): 269-274.
[16] Wang Y K, Wang L, Ni Q, et al. Non-planar responses of cantilevered pipes conveying fluid with intermediate motion constraints [J]. Nonlinear Dynamics, 2018, 93(2): 505-524.
[17] Zhang H M, Xing Y F. A framework of time integration methods for nonsmooth systems with unilateral constraints [J]. Applied Mathematics and Computation, 2019, 363(C).
[18] Peng H J, Song N N, Kan Z Y. A nonsmooth contact dynamic algorithm based on the symplectic method for multibody system analysis with unilateral constraints [J]. Multibody System Dynamics, 2020, 49(2): 119-153.
[19] Miao P C, Li D H, Yue Y, et al. Chaotic attractor of the normal form map for grazing bifurcations of impact oscillators [J]. Physica D: Nonlinear Phenomena, 2019, 398: 164-170.
[20] Gritli H , Belghith S. Diversity in the nonlinear dynamic behavior of a one-degree-of-freedom impact mechanical oscillator under OGY-based state-feedback control law: Order, chaos and exhibition of the border-collision bifurcation [J]. Mechanism and Machine Theory, 2017, 124: 1-41.
[21] Reboucas G F S, Santos I F, Thomsen J J. Unilateral vibro-impact systems—Experimental observations against theoretical predictions based on the coefficient of restitution [J]. Journal of Sound and Vibration, 2018, 440: 346-371.
[22] Guo X Y, Zhang G, Tian R L. Periodic solution of a non-smooth double pendulum with unilateral rigid constrain [J]. Symmetry, 2019, 11(7): 886-886.
[23] 王乙坤，王琳，倪樵，等. 具有刚性间隙约束输流管的碰撞振动[J]. 力学学报，2020, 52(5): 1498-1508.
WANG Yi-kun, WANG Lin, NI Qiao, et al. Vibro-impact dynamics of pipe conveying fluid subjected to rigid clearance constraint [J]. Chinese Journal of Theoretical and Applied Mechani, 2020, 52(5): 1498-1508.
[24] Shampine L F, Reichelt M W. The MATLAB ODE suite [J]. The SIAM Journal on Scientific Computing, 1997, 18(1): 1-22.
[25] Shampine L F, Reichelt M W, Kierzenka J A. Solving index-1 DAEs in MATLAB and Simulink [J]. SIAM Review, 1999, 41(3): 538-552.
[26] Wagg D J, Bishop S R. Application of non-smooth modelling techniques to the dynamics of a flexible impacting beam. Journal of Sound and Vibration, 2002, 256(5): 803-820.
[27] Lu Z Q, Zhang K K, Ding H, et al. Internal resonance and stress distribution of pipes conveying fluid in supercritical regime [J]. International Journal of Mechanical Sciences, 2020, 186.
[28] Zhou J, Chang X P, Xiong Z J, et al. Stability and nonlinear vibration analysis of fluid-conveying composite pipes with elastic boundary conditions [J]. Thin-Walled Structures, 2022, 179.
[29] 方孟孟，郭长青. 悬臂输流管道在基础激励与脉动内流联合作用下的参激振动[J]. 应用力学学报，2020, 37(2): 653-660.
FANG Meng-meng, GUO Chang-qing. Parametric vibration of cantilever pipes under combined action of foundation excitation and pulsating internal flow [J]. Chinese Journal of Applied Mechanics. 2020, 37(2): 653-660+933-934.
[30] Alidousti J, Eskandari Z. Dynamical behavior and Poincare section of fractional-order centrifugal governor system [J]. Mathematics and Computers in Simulation, 2021, 182: 791-806.
[31] 吕小红. 冲击振动系统的粘滞振动及分岔特性研究[D]. 兰州：兰州交通大学，2016.
LV Xiao-hong. Research on sticking vibration and bifurcation characteristics of vibro-impact system [D]. Lanzhou: Lanzhou Jiaotong University, 2016.
[32] 王世俊，同长虹，罗冠炜. 含多刚性约束的两自由度振动系统的动力学特性分析[J]. 振动与冲击，2021, 40(06): 11-22+78.
WANG Shi-jun, TONG Chang-hong, LUO Guan-wei. Dynamic characteristics of a two-degree-of-freedom vibration system with multiple rigid constraints [J]. Journal of Vibration and Shock, 2021, 40(06): 11-22+78.
[33] Lyu X H, Gao Q F, Luo G W. Dynamic characteristics of a mechanical impact oscillator with a clearance [J]. International Journal of Mechanical Sciences, 2020, 178 (prepublish): 105605-105605.
[34] Li G F, Wu S P, Wang H B, et al. Global behavior of a simplified model for the micro-vibration molding machine in parameter-state space [J]. Mechanism and Machine Theory, 2020, 154.