弹性地基上输流管道的静态和动态稳定性研究
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摘要
研究了Pasternak双参数弹性地基上两端固定输流管道的静态和动态稳定性问题。利用复模态方法计算了系统的固有频率和临界流速,并应用平均法得到了脉动内流作用时管道的前两阶主参数共振和组合共振区域,讨论了地基的线性刚度、剪切刚度及一些管道参数对系统稳定性的影响。结果表明:改变两个地基刚度均可以影响系统的静态和动态稳定性,但剪切刚度的作用更显著,不能忽略;同时管道预紧力、流体介质与管道质量比、粘弹性系数和管内介质平均流速等管道参数也会对系统的稳定性产生一定的影响。
Static and dynamic stabilities of clamped-clamped fluid pipes are investigated. The pipes rest on Pasternak-type two-parameter elastic foundations. Applying the complex mode method, the natural frequencies and critical flow velocity are calculated. For the case of pulsating inner flow, regions of principal parametric resonances for the first two modes and the combination resonance are obtained using the averaging method. The contributions of the linear and sheer foundation rigidities as well as some pipe parameters on the stabilities of the system are discussed. The results demonstrate that the variation of foundation rigidities can influence both the static and dynamic stabilities, and the effect of the sheer rigidity is much greater than that of the linear rigidity and can’t be neglected; moreover, some pipe parameters such as tension force, mass ratio of fluid to pipe, viscoelastic coefficient and mean flow velocity have some impacts on the stabilities of the system.
Static and dynamic stabilities of clamped-clamped fluid pipes are investigated. The pipes rest on Pasternak-type two-parameter elastic foundations. Applying the complex mode method, the natural frequencies and critical flow velocity are calculated. For the case of pulsating inner flow, regions of principal parametric resonances for the first two modes and the combination resonance are obtained using the averaging method. The contributions of the linear and sheer foundation rigidities as well as some pipe parameters on the stabilities of the system are discussed. The results demonstrate that the variation of foundation rigidities can influence both the static and dynamic stabilities, and the effect of the sheer rigidity is much greater than that of the linear rigidity and can’t be neglected; moreover, some pipe parameters such as tension force, mass ratio of fluid to pipe, viscoelastic coefficient and mean flow velocity have some impacts on the stabilities of the system.
引文
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[3]梁峰,金基铎,杨晓东,闻邦椿.输流管道参数共振的试验研究[J].振动、测试与诊断,2008,28(4):315―317.Liang Feng,Jin Jiduo,Yang Xiaodong,Wen Bangchun.Experimental investigation on parametric resonances of a fluid-conveying pipe[J].Journal of Vibration,Measurement&Diagnosis,2008,28(4):315―317.(in Chinese)
[4]Padoussis M P,Li G X,Moon F C.Chaotic oscillations of the autonomous system of a constrained pipeconveying fluid[J].Journal of Sound and Vibration,1989,135(1):1―19.
[5]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[J].力学学报,2002,34(6):863―873.Jin Jiduo,Zou Guangsheng,Zhang Yufei.Bifurcations and chaotic motions of a cantilevered pipe conveying fluid[J].Chinese Journal of Theoretical and Applied Mechanics,2002,34(6):863―873.(in Chinese)
[6]Impollonia N,Elishakoff I.Effect of elastic foundations on divergence and flutter of an articulated pipe conveying fluid[J].Journal of Fluids and Structures,2000,14(4):559―573.
[7]Qian Qin,Wang Lin,Ni Qiao.Nonlinear responses of a fluid-conveying pipe embedded in nonlinear elastic foundations[J].Acta Mechanica Solida Sinica,2008,21(2):170―176.
[8]包日东,闻邦椿.地震载荷作用下液化土中输流管道动态响应研究[J].工程力学,2008,25(6):170―175.Bao Ridong,Wen Bangchun.Study of seismic response for pipeline conveying fluid in liquefaction soil[J].Engineering Mechanics,2008,25(6):170―175.(in Chinese)
[9]Dutta S C,Roy R.A critical review on idealization and modeling for interacion among soil-foundation-structure system[J].Computers&Structures,2002,80(20-21):1579―1594.
[10]王小龙,姚安林.埋地钢管局部悬空的挠度和内力分析[J].工程力学,2008,25(8):218―222.Wang Xiaolong,Yao Anlin.Deflection and internal force analysis of buried steel pipelines in partial hanging[J].Engineering Mechanics,2008,25(8):218―222.(in Chinese)
[11]龚耀清,包世华.超高层建筑空间巨型框架自由振动计算的新方法[J].工程力学,2008,25(10):133―140.Gong Yaoqing,Bao Shihua.A new method for free vibration analysis of space mega frame of super tall buildings[J].Engineering Mechanics,2008,25(10):133―140.(in Chinese)
[12]DoaréO,de Langre E.Local and global instability of fluid-conveying pipes on elastic foundations[J].Journal of Fluids and Structures,2002,16(1):1―14.
[13]王忠民,张战午,李会侠.弹性地基上输送振荡流粘弹性管道的动力稳定性[J].机械工程学报,2005,41(10):57―60.Wang Zhongmin,Zhang Zhanwu,Li Huixia.Dynamic stability of viscoelastic pipes conveying pulsating fluid on the elastic foundation[J].Chinese Journal of Mechanical Engineering,2005,41(10):57―60.(in Chinese)
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