分布随从力作用的双参数地基上悬臂管稳定性研究

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。

Stability of Cantilever Pipe Conveying Fluid with Distributed Follower Force on Two-parameter Foundation

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.