具有刚性间隙约束输流管的碰撞振动

王乙坤; 王琳; 倪樵; 杨沫; 刘德政; 秦涛

doi:10.6052/0459-1879-20-137

具有刚性间隙约束输流管的碰撞振动

王乙坤^*†2), ,,
王琳^†3),,
倪樵^†,
杨沫^*,
刘德政^*,
秦涛^*

^*湖北文理学院机械工程学院,湖北襄阳 441053
^†华中科技大学力学系,武汉 430074

基金项目: 1)国家自然科学基金(11902112);国家自然科学基金(11972167);“机电汽车”湖北省优势特色学科群开放基金(XKQ2019008)

详细信息

通讯作者:
王乙坤

王乙坤,王琳

中图分类号: O322
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出版历程
- 收稿日期: 2020-04-06
- 刊出日期: 2020-10-09

VIBRO-IMPACT DYNAMICS OF PIPE CONVEYING FLUID SUBJECTED TO RIGID CLEARANCE CONSTRAINT

Wang Yikun^*†2), ,,
Wang Lin^†3),,
Ni Qiao^†,
Yang Mo^*,
Liu Dezheng^*,
Qin Tao^*

^*School of Mechanical Engineering,Hubei University of Arts and Science,Xiangyang 441053,Hubei,China
^†Department of Mechanics,Huazhong University of Science and Technology,Wuhan 430074,China

摘要

摘要: 管道与间隙约束间的碰撞振动是工程输流管结构的一个重要动力学现象. 迄今,人们通常采用光滑的非线性弹簧来模拟管道与间隙约束之间的碰撞力,但这种光滑的碰撞力无法真实反映碰撞前后管道状态向量的非光滑传递特征. 本文基于非光滑理论建立了具有刚性间隙约束简支输流管的非线性碰撞振动模型,利用 Galerkin 法离散了无穷维的管道模型, 并引入恢复系数构造了碰撞前后管道各处状态向量的传递矩阵,运用四阶龙格库塔法分析了脉动内流激励下管道与刚性间隙约束的非光滑碰撞振动现象,着重讨论了刚性间隙约束参数对管道动态响应随流速脉动频率变化的影响规律,特别是碰撞振动的周期性运动规律. 研究结果表明,刚性约束间隙值对管道碰撞振动行为的影响较大,在某些脉动频率下管道会出现多周期和非周期性的运动形态,还可出现非光滑系统特有的黏滑现象. 此外,碰撞恢复系数对管道振动的影响也比较显著,较小的恢复系数值更容易使管道在大范围脉动频率区间出现复杂的非周期碰撞振动.
- 输流管 /
- 刚性间隙约束 /
- 碰撞振动 /
- 分岔 /
- 黏滑运动
Abstract: The vibro-impact dynamics due to loose constraints have become one of the key scientific problems in the dynamical system of pipes conveying fluid. The impact force modeled by smoothed nonlinear springs varies continuously with time and displacement of the vibrating pipe, which cannot exactly capture the non-smooth characteristics of the saltation of state vectors for the pipes before and after an impact. In this paper, a non-smooth mathematical model of simply supported pipes conveying pulsating fluid, subjected to a rigid constraint somewhere along the pipe length is established, with consideration of the effect of the values of clearance and coefficient of restitution of the constraint. Especially, the periodic and aperiodic oscillations are investigated under various pulsating frequencies of the internal fluid. The transition matrices of the displacement and velocity of all nodes along the pipe before and after impact were derived based on a Galerkin's approach. The nonlinear equations of motion are solved via a fourth-order Runge-Kutta method, by applying the impact boundary conditions. Results show that the pipe is capable of displaying interesting vibro-impact behaviors in the presence of the rigid clearance constraint with the variation of pulsating frequency of the flowing fluid. With a clearance close to the maximum displacement of the pipe without constraint, periodic vibro-impact behaviors are observed with multiple impacts. The vibration velocities before the pipe impacts on the edge of the rigid clearance constraint decrease to zero gradually with the displacement invariant, which is called a dynamical stick-slip motion, also known as a typical non-smooth phenomenon. By decreasing the value of coefficient of restitution, the responses of the pipe may change from periodic vibrations to chaotic ones. This work provides an attractive strategy for further understanding of the nonlinear impact dynamics of pipes conveying fluid subjected to rigid clearance constraint based on non-smooth theories.
- pipe conveying fluid /
- rigid clearance constraint /
- vibro-impact /
- bifurcation /
- sticking motion

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参考文献(1)

[1]	徐鉴, 杨前彪. 输液管模型及其非线性动力学近期研究进展. 力学进展, 2004,34(2):182-194
[1]	( Xu Jian, Yang Qianbiao. Recent development on models and nonlinear dynamics of pipes conveying fluid. Advances in Mechamics, 2004,34(2):182-194 (in Chinese))
[2]	徐鉴, 王琳. 输流管动力学分析和控制. 北京: 科学出版社, 2015
[2]	( Xu Jian, Wang Lin. Dynamics and Control of Fluid-Conveying Pipe Systems. Beijing, Science Press, 2015 (in Chinese))
[3]	金基铎, 邹光胜, 张宇飞. 悬臂输流管道的运动分岔现象和混沌运动. 力学学报, 2002,34(6):863-873
[3]	( Jin Jiduo, Zou Guangsheng, Zhang Yufei. Bifurcations and chaotic motions of a cantilevered pipe conveying fluid. Chinese Journal of Theoretical and Applied Mechanics, 2002,34(6):863-873 (in Chinese))
[4]	王乙坤, 王琳. 分布式运动约束下悬臂输液管的参数共振研究. 力学学报, 2019,51(2):558-568
[4]	( Wang Yikun, Wang Lin. Parametric resonance of a cantilevered pipe conveying fluid subjected to distributed motion constraints. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(2):558-568 (in Chinese))
[5]	Modarres-Sadeghi Y, Paidoussis MP, Semler C. Three-dimensional oscillations of a cantilever pipe conveying fluid. International Journal of Non-Linear Mechanics, 2008,43(1):18-25
[6]	Modarres-Sadeghi Y, Paidoussis MP. Nonlinear dynamics of extensible fluid-conveying pipes, supported at both ends. Journal of Fluids and Structures, 2009,25(3):535-543
[7]	Paidoussis MP. Fluid-Structure Interactions: Slender Structures and Axial Flow. 2 ed. San Diego: Elsevier Academic Press, 2014
[8]	Paidoussis MP, Semler C. Nonlinear and chaotic oscillations of a constrained cantilevered pipe conveying fluid: A full nonlinear analysis. Nonlinear Dynamics, 1993,4(6):655-670
[9]	Ghayesh MH, Paidoussis MP. Three-dimensional dynamics of a cantilevered pipe conveying fluid, additionally supported by an intermediate spring array. International Journal of Non-Linear Mechanics, 2010,45(5):507-524
[10]	Ghayesh MH, Pa$\check{i}$doussis MP, Modarres-Sadeghi Y. Three-dimensional dynamics of a fluid-conveying cantilevered pipe fitted with an additional spring-support and an end-mass. Journal of Sound and Vibration, 2011,330(12):2869-2899
[11]	Paidoussis MP, Li GX, Moon FC. Chaotic oscillations of the autonomous system of a constrained pipe conveying fluid. Journal of Sound and Vibration, 1989,135(1):1-19
[12]	Sadath A, Dixit HN, Vyasarayani CP. Dynamics of cross-flow heat exchanger tubes with multiple loose supports. Journal of Pressure Vessel Technology, 2016,138(5):051303
[13]	Hassan MA, Weaver DS, Dokainish MA. A new tube/support impact model for heat exchanger tubes. Journal of Fluids and Structures, 2005,21(5-7):561-577
[14]	Hassan M, Mohany A. Fluidelastic instability modeling of loosely supported multispan U-tubes in nuclear steam generators. Journal of Pressure Vessel Technology, 2013,135(1):011306
[15]	Hassan MA, Weaver DS, Dokainish MA. The effects of support geometry on the turbulence response of loosely supported heat exchanger tubes. Journal of Fluids and Structures, 2003,18(5):529-554
[16]	Azizian R. Dynamic Modeling of Tube-Support Interaction in Heat Exchangers. école Polytechnique de Montréal, 2012
[17]	张艳雷, 黄慧春, 陈立群. 振荡流作用下受约束的悬臂输流管的分岔特性. 噪声与振动控制, 2012,32(5):46-48
[17]	( Zhang Yanlei, Huang Huichun, Chen Liqun. Bifurcation analysis of a constrained cantilevered pipe conveying fluid under the harmonic parametric excitations. Noise and Vibration Control, 2012,32(5):46-48 (in Chinese))
[18]	王乙坤, 倪樵, 王琳等. 具有松动约束悬臂输液管的三维非线性振动. 科学通报, 2017,62(36):4270-4277
[18]	( Wang Yikun, Ni Qiao, Wang Lin, et al. Three-dimensional nonlinear dynamics of a cantilevered pipe conveying fluid subjected to loose constraints. Chinese Science Bulletin, 2017,62(36):4270-4277 (in Chinese))
[19]	Yang XD, An HZ, Qian YJ, et al. A comparative analysis of modal motions for the gyroscopic and non-gyroscopic two degree-of-freedom conservative systems. Journal of Sound and Vibration, 2016,385:300-309
[20]	Yang XD, An HZ, Qian YJ, et al. Elliptic motions and control of rotors suspending in active magnetic bearings. ASME Journal of Computational and Nonlinear Dynamics, 2016,11(5):054503
[21]	Geng X, Ding H, Wei K, et al. Suppression of multiple modal resonances of a cantilever beam by an impact damper. Applied Mathematics and Mechanics, 2020,41(3):383-400
[22]	Budd C, Dux F, Cliffe A. The effect of frequency and clearance variations on single-degree-of-freedom impact oscillators. Journal of Sound & Vibration, 1995,183(4):475-502
[23]	金栋平, 胡海岩. 碰撞振动及其典型现象. 力学进展, 1999,29(2):155-163
[23]	( Jin Dongping, Hu Haiyan. Vibro-impacts and their typical behaviors of mechanical systems. Advances in Mechanics, 1999,29(2):155-163 (in Chinese))
[24]	Li QH, Tan JY. Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops. Chinese Physics B, 2011,20(4):123-131
[25]	Guo X, Zhang G, Tian R. Periodic solution of a non-smooth double pendulum with unilateral rigid constrain. Symmetry, 2019,11(7):886
[26]	秦志英, 李群宏. 一类非光滑映射的边界碰撞分岔. 力学学报, 2013,45(1):25-29.
[26]	( Qin Zhiying, Li Qunhong. Border-collision bifurcation in a kind of non-smooth maps. Chinese Journal of Theoretical and Applied Mechanics, 2013,45(1):25-29 (in Chinese))
[27]	罗冠炜, 谢建华. 碰撞振动系统的周期运动和分岔. 北京: 科学出版社, 2004
[27]	( Luo Guanwei, Xie Jianhua. Periodic motions and bifurcations of vibrio-impact systems. Beijing: Science Press, 2004 (in Chinese))
[28]	Luo G, Xie J, Zhu X, et al. Periodic motions and bifurcations of a vibro-impact system. Chaos, Solitons & Fractals, 2008,36(5):1340-1347
[29]	Yue Y, Xie JH. Symmetry and bifurcations of a two-degree-of-freedom vibro-impact system. Journal of Sound and Vibration, 2008,314(1-2):228-245
[30]	Li Q, Chen Y, Wei Y, et al. The analysis of the spectrum of Lyapunov exponents in a two-degree-of-freedom vibro-impact system. International Journal of Non-Linear Mechanics, 2011,46(1):197-203
[31]	李群宏, 陈玉明. 双侧约束对碰系统 Lyapunov 指数分析. 振动与冲击, 2012,31(7):148-152
[31]	( Li Qunhong, Chen Yuming. Analysis of the Lyapunov exponential spectrum in a vibro-impact system with two-sided rigid stops. Journal of Vibration and Shock, 2012,31(7):148-152 (in Chinese))
[32]	Wagg DJ, Bishop SR. Application of non-smooth modelling techniques to the dynamics of a flexible impacting beam. Journal of Sound and Vibration, 2002,256(5):803-820
[33]	Jin JD, Song ZY. Parametric resonances of supported pipes conveying pulsating fluid. Journal of Fluids and Structures, 2005,20(6):763-783
[34]	Panda LN, Kar RC. Nonlinear dynamics of a pipe conveying pulsating fluid with combination, principal parametric and internal resonances. Journal of Sound and Vibration, 2008,309(3-5):375-406
[35]	Wang L. A further study on the non-linear dynamics of simply supported pipes conveying pulsating fluid. International Journal of Non-Linear Mechanics, 2009,44(1):115-121
[36]	Li C, Xu W, Wang L, et al. Impulsive control of sticking motion in van der Pol one-sided constraint system. Applied Mathematics and Computation, 2014,248:363-370

施引文献(16)

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