含非线性能量汇的简支输液管非线性振动控制研究
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摘要
论文建立了一个含有非线性能量汇(NES)装置并输运脉动内流的简支输液管道理论模型,研究了NES装置对管道的非线性动力学特性与振动控制的影响.利用Galerkin和龙格库塔法,得到了在含NES和不含NES装置时管道动力学响应的数值结果.研究表明, NES装置能有效地抑制管道振动.通过对比可知, NES对管道系统的稳定性和非线性振动控制有着明显的影响.此外,论文还详细讨论了NES装置相关参数对系统的动力学影响.结果表明,增大NES的弹簧刚度k、阻尼σ和质量比ε有利于管道减振,且最佳安装位置在管道中点.此外,增大阻尼σ能缩小失稳激励频率区域,而其他参数的变化对失稳激励频率区域影响较小.
Pipes conveying fluid are widely applied in heat exchanger systems, nuclear power plants, chemical process plants, marine risers, etc. However, the excessive piping vibration can cause leaks, fatigue failures and noises. Thus, investigations on the vibration suppression of pipes are of theoretical and practical significance. In this study, we construct a theoretical model to investigate the nonlinear dynamics of a simply-supported pipe conveying pulsating fluid equipped with a nonlinear energy sink(NES). By taking the deflection-dependent axial force into consideration, the nonlinear governing equations of the system are obtained. Based on the Galerkin method and the Runge-Kutta algorithm, the resulting equations are discretized and solved. Numerical results for the nonlinear dynamical responses of the pipes with and without NES are presented. It is found that pipe vibration can be effectively suppressed by the NES. Comparing with the pipe without NES under the same condition, the stability and nonlinear vibration characteristics of the pipe are greatly affected when the NES is attached. The effects of NES parameters on the stability and vibration response of the system are elaborately addressed. Numerical results show that an increase in the nonlinear(cubic) stiffness k, dissipation σ or mass ratio ε can improve the suppression of pipe vibration; and the improvement in the suppression of pipe vibration by increasing dissipation σ is more significant than those by increasing other NES parameters. It shows that the best mounting position for the NES to reduce pipe vibration is at the midpoint of the pipe. In addition, it is found that an increase in dissipation σ can shrink the unstable region in the frequency domain, while other NES parameters have little effects on the instability. Therefore, dissipation σ is the most effective parameter for the nonlinear energy sink to control the vibration of pipes conveying fluid.
Pipes conveying fluid are widely applied in heat exchanger systems, nuclear power plants, chemical process plants, marine risers, etc. However, the excessive piping vibration can cause leaks, fatigue failures and noises. Thus, investigations on the vibration suppression of pipes are of theoretical and practical significance. In this study, we construct a theoretical model to investigate the nonlinear dynamics of a simply-supported pipe conveying pulsating fluid equipped with a nonlinear energy sink(NES). By taking the deflection-dependent axial force into consideration, the nonlinear governing equations of the system are obtained. Based on the Galerkin method and the Runge-Kutta algorithm, the resulting equations are discretized and solved. Numerical results for the nonlinear dynamical responses of the pipes with and without NES are presented. It is found that pipe vibration can be effectively suppressed by the NES. Comparing with the pipe without NES under the same condition, the stability and nonlinear vibration characteristics of the pipe are greatly affected when the NES is attached. The effects of NES parameters on the stability and vibration response of the system are elaborately addressed. Numerical results show that an increase in the nonlinear(cubic) stiffness k, dissipation σ or mass ratio ε can improve the suppression of pipe vibration; and the improvement in the suppression of pipe vibration by increasing dissipation σ is more significant than those by increasing other NES parameters. It shows that the best mounting position for the NES to reduce pipe vibration is at the midpoint of the pipe. In addition, it is found that an increase in dissipation σ can shrink the unstable region in the frequency domain, while other NES parameters have little effects on the instability. Therefore, dissipation σ is the most effective parameter for the nonlinear energy sink to control the vibration of pipes conveying fluid.
引文
[1] Pa?doussis M P. Fluid-structure Interactions: Slender Structures and Axial Flow [M]. Academic Press, 1998.
[2] Pa?doussis M P, Issid N T. Dynamic stability of pipes conveying fluid[J]. Journal of Sound and Vibration, 1974, 33 (3): 267-294.
[3] 徐鉴,王琳. 输液管动力学分析和控制[M]. 北京:科学出版社, 2015.(Xu J, Wang L. Dynamics and Control of Fluid-conveying Pipe Systems [M]. Beijing: Science Press, 2015. (in Chinese))
[4] Jin J D. Stability and chaotic motions of a restrained pipe conveying fluid[J]. Journal of Sound & Vibration, 1997, 208 (3): 427-439.
[5] Yau C H, Bajaj A K,Nwokah O D I. Active control of chaotic vibration in a constrained flexible pipe conveying fluid[J]. Journal of Fluids and Structures, 1995, 9 (1): 99-122.
[6] Doki H, Hiramoto K, Skelton R E. Active control of cantilevered pipes conveying fluid with constraints on input energy[J]. Journal of Fluids and Structures, 1998, 12 (5): 615-628.
[7] Tsai Y K, Lin Y H. Adaptive modal vibration control of a fluid-conveying cantilever pipe[J]. Journal of Fluids and Structures, 1997, 11 (5): 535-547.
[8] Rinaldi S, Pa?doussis M P. Dynamics of a cantilevered pipe discharging fluid, fitted with a stabilizing end-piece[J]. Journal of Fluids & Structures, 2010, 26 (3): 517-525.
[9] Yu D, Wen J, Zhao H, Liu Y, Wen X. Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid[J]. Journal of Sound and Vibration, 2008, 318 (1): 193-205.
[10] Vakakis A F. Inducing passive nonlinear energy sinks in vibrating systems[J]. Journal of Vibration & Acoustics, 2001, 123 (3): 324-332.
[11] Lee Y S,Vakakis A F, Bergman L A, McFarland D M, Kerschen G, Nucera F, Tsakirtzis S, Panagopoulos P N. Passive non-linear targeted energy transfer and its applications to vibration absorption: A review[J]. Proceedings of the Institution of Mechanical Engineers Part K Journal of Multi-body Dynamics, 2008, 222 (2): 322-329.
[12] Vakakis A F, Manevitch L I, Gendelman O, Bergman L. Dynamics of linear discrete systems connected to local, essentially non-linear attachments[J]. Journal of Sound and Vibration, 2003, 264 (3): 559-577.
[13] Panagopoulos P N,Vakakis A F,Tsakirtzis S. Transient resonant interactions of finite linear chains with essentially nonlinear end attachments leading to passive energy pumping[J]. International Journal of Solids & Structures, 2004, 41 (22): 6505-6528.
[14] Starosvetsky Y,Gendelman O V. Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning[J]. Journal of Sound & Vibration, 2008, 315 (3): 746-765.
[15] Yang T Z,Yang X D, Li Y, Fang B. Passive and adaptive vibration suppression of pipes conveying fluid with variable velocity[J]. Journal of Vibration and Control, 2013, 20 (9): 1293-1300.
[16] Zhang Y W, Zhang Z, Chen L Q, Yang T Z, Fang B, Zang J. Impulse-induced vibration suppression of an axially moving beam with parallel nonlinear energy sinks[J]. Nonlinear Dynamics, 2015, 82(1-2): 61-71.
[17] Duan N, Fang B, Teng Y. Passive vibration control of pipes conveying fluid with parallel nonlinear energy sinks[J]. DEStech Transactions on Computer Science and Engineering, 2017,407-412.
[18] Mamaghani A E, Khadem S E, Bab S. Vibration control of a pipe conveying fluid under external periodic excitation using a nonlinear energy sink[J]. Nonlinear Dynamics, 2016, 86(3):1-35.
[19] Zhou K, Xiong F R, Jiang N B, Dai H L, Yan H, Wang L, Ni Q. Nonlinear vibration control of a cantilevered fluid-conveying pipe using the idea of nonlinear energy sink[J]. Nonlinear Dynamics, 2018,1-22.
[2] Pa?doussis M P, Issid N T. Dynamic stability of pipes conveying fluid[J]. Journal of Sound and Vibration, 1974, 33 (3): 267-294.
[3] 徐鉴,王琳. 输液管动力学分析和控制[M]. 北京:科学出版社, 2015.(Xu J, Wang L. Dynamics and Control of Fluid-conveying Pipe Systems [M]. Beijing: Science Press, 2015. (in Chinese))
[4] Jin J D. Stability and chaotic motions of a restrained pipe conveying fluid[J]. Journal of Sound & Vibration, 1997, 208 (3): 427-439.
[5] Yau C H, Bajaj A K,Nwokah O D I. Active control of chaotic vibration in a constrained flexible pipe conveying fluid[J]. Journal of Fluids and Structures, 1995, 9 (1): 99-122.
[6] Doki H, Hiramoto K, Skelton R E. Active control of cantilevered pipes conveying fluid with constraints on input energy[J]. Journal of Fluids and Structures, 1998, 12 (5): 615-628.
[7] Tsai Y K, Lin Y H. Adaptive modal vibration control of a fluid-conveying cantilever pipe[J]. Journal of Fluids and Structures, 1997, 11 (5): 535-547.
[8] Rinaldi S, Pa?doussis M P. Dynamics of a cantilevered pipe discharging fluid, fitted with a stabilizing end-piece[J]. Journal of Fluids & Structures, 2010, 26 (3): 517-525.
[9] Yu D, Wen J, Zhao H, Liu Y, Wen X. Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid[J]. Journal of Sound and Vibration, 2008, 318 (1): 193-205.
[10] Vakakis A F. Inducing passive nonlinear energy sinks in vibrating systems[J]. Journal of Vibration & Acoustics, 2001, 123 (3): 324-332.
[11] Lee Y S,Vakakis A F, Bergman L A, McFarland D M, Kerschen G, Nucera F, Tsakirtzis S, Panagopoulos P N. Passive non-linear targeted energy transfer and its applications to vibration absorption: A review[J]. Proceedings of the Institution of Mechanical Engineers Part K Journal of Multi-body Dynamics, 2008, 222 (2): 322-329.
[12] Vakakis A F, Manevitch L I, Gendelman O, Bergman L. Dynamics of linear discrete systems connected to local, essentially non-linear attachments[J]. Journal of Sound and Vibration, 2003, 264 (3): 559-577.
[13] Panagopoulos P N,Vakakis A F,Tsakirtzis S. Transient resonant interactions of finite linear chains with essentially nonlinear end attachments leading to passive energy pumping[J]. International Journal of Solids & Structures, 2004, 41 (22): 6505-6528.
[14] Starosvetsky Y,Gendelman O V. Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning[J]. Journal of Sound & Vibration, 2008, 315 (3): 746-765.
[15] Yang T Z,Yang X D, Li Y, Fang B. Passive and adaptive vibration suppression of pipes conveying fluid with variable velocity[J]. Journal of Vibration and Control, 2013, 20 (9): 1293-1300.
[16] Zhang Y W, Zhang Z, Chen L Q, Yang T Z, Fang B, Zang J. Impulse-induced vibration suppression of an axially moving beam with parallel nonlinear energy sinks[J]. Nonlinear Dynamics, 2015, 82(1-2): 61-71.
[17] Duan N, Fang B, Teng Y. Passive vibration control of pipes conveying fluid with parallel nonlinear energy sinks[J]. DEStech Transactions on Computer Science and Engineering, 2017,407-412.
[18] Mamaghani A E, Khadem S E, Bab S. Vibration control of a pipe conveying fluid under external periodic excitation using a nonlinear energy sink[J]. Nonlinear Dynamics, 2016, 86(3):1-35.
[19] Zhou K, Xiong F R, Jiang N B, Dai H L, Yan H, Wang L, Ni Q. Nonlinear vibration control of a cantilevered fluid-conveying pipe using the idea of nonlinear energy sink[J]. Nonlinear Dynamics, 2018,1-22.