为了对分布随从力作用时双参数地基上悬臂管稳定性进行分析,利用Euler-Bernoulli梁模型创立输流管道的运动微分方程,然后运用传递矩阵法进行求解。通过分析悬臂输流管的无量纲复频率和失稳时临界流速间的关系,在地基刚度取4种不同值情况下研究悬臂管道受分布随从力和流体流速作用时的振动情况。结果表明①地基刚度取值一定时,悬臂管道受分布随从力和流体流速影响时的振动特点大不一样;②无量纲分布随从力与流体流速取值一定时,管道系统的振动状况随着地基刚度增加而更加稳定,相比线性刚度的影响剪切刚度的作用尤为突出。
Abstract
Through analyzing the relationship between dimensionless complex frequency and critical flow velocity of cantilever pipe, the stability of cantilever pipe conveying fluid with distributed follower force on two-parameter elastic foundation was researched. The vibration of the cantilever pipe under actions of distributed follower force and flow velocity with four different values of foundation stiffness were also analyzed. On the basis of Euler-Bernoulli beam model, differential motion equations of pipes were established and the equations were solved by using transfer matrix method. Results show that 1) with given foundation stiffness, vibration characteristics of the cantilever pipes under the action of distributed follower force is obviously different from that of fluid velocity; 2) with given dimensionless distributed follower force and fluid velocity, the bigger foundation stiffness is, the more stable vibration condition of the pipes system is. In addition, the influence of shear stiffness is more obvious than that of linear stiffness.
关键词
双参数地基 /
分布随从力 /
悬臂输流管道 /
地基刚度 /
无量纲分布
Key words
two-parameter foundation /
distributed follower force /
cantilever pipes conveying fluid /
foundation stiffness /
dimensionless distribution
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] WINKLER E. Die Lehre Von Der Elasticitat Und Festigkeit [M]. Prague:Dominicus, 1867.
[2] SELVADURAI A P S. Elastic Analysis of Soil Foundation Interaction [M]. London: Elesvier Scientific Publishing Company, 1979.
[3] 梁 峰, 李伟杰, 杨晓东,等. Winkler地基上输流管道的临界流速分析[J]. 机械强度, 2011, 33(1): 20-23.
[4] 包日东,冯 颖,郝 敏. 不同支承条件下梁结构弯曲振动的固有特性[J]. 机械设计与制造,2009,(9): 83-86.
[5] 彭 震, 陆海翔, 杨志安. Winkler地基梁在温度场中受简谐激励作用下的主共振和主参数共振分析[J]. 机械强度, 2007, 29(4): 695-698.
[6] DUTTA S C, ROY R. A Critical Review on Idealization and Modeling for Interaction Among Soil-foundation-structure System[J].Computer & Structure,2002,80(20/21):1579-1594.
[7] 梁 峰, 金基铎, 杨晓东,等. 弹性地基上输流管道的静态和动态稳定性研究[J]. 工程力学, 2011, 27(11): 166-171.
[8] 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.
[9] 马小强, 向 宇, 黄玉盈. 求解弹性地基上任意支承输液直管稳定性问题的传递矩阵法[J]. 工程力学. 2004, 21(4): 194-198.
[10]HAUGER W, VETTER K. Influence of an Elastic Foundation on the Stability of a Tangentially Loaded Column [J]. Journal of Sound and Vibration, 1976,47 (2):296-299.
[11]CHELLAPILLA K R, SIMHAB H S. Vibrations of Fluid-Conveying Pipes Resting on Two-parameter Foundation [J]. The Open Acoustics Journal, 2008, 1(1):24-33.
[12]郭长青,刘红涛,王晓峰,等. 输流管道在分布随从力作用下的振动和稳定性[J]. 工程力学, 2010, 27(4): 190-196.
[13]DJONDJOROV P A. On the Critical Velocities of Pipes on Variable Elastic Foundations [J]. Journal of Sound and Vibration, 2001, 16(3): 201-208.
[14]LEE D M, CHOI M J, OH T Y. Transfer Matrix Modeling for the 3-Dimensional Vibration Analysis of Piping System Containing Fluid Flow [J]. Journal of Mechanical Science and Technology,1996,10(2): 180-189.
PDF(2209 KB)
