分析弹性地基一般支承输流管道的动力学特性

Dynamic characteristics of commonly supported fluid-conveying pipes on elastic foundation

研究Pasternak双参数地基一般支承输流管道的线性固有频率及非线性动力学特性。综合考虑管道黏弹性系数、地基的剪切效应、线性刚度的影响,建立了系统运动微分方程。根据两端一般支承的边界条件推导出线性系统固有频率方程,分析了基础激励与脉动流作用下,流速对系统非线性动力学特性的影响。数值结果表明,管道一阶临界流速随弹性系数的增大呈现先增大后减小的趋势,当弹性系数足够大时,管道随流速的增加发生一阶、二阶模态耦合现象;系统响应随流速变化呈现由倍周期分岔过渡到混沌运动的特性;当管内流体流速足够大时,系统响应保持混沌运动状态。

The linear natural frequencies and nonlinear dynamic characteristics of a fluid-conveying pipe under commonly supported conditions on Pasternak-type two-parameter elastic foundation were investigated. Synthetically considering viscoelastic coefficient of pipe,and influences of shear effect and linear stiffness of foundation,the differential equations of motion of the piping system were established. The natural frequency equation of the linear piping system was derived with the commonly supported boundary condition. The effects of flow velocity on the nonlinear dynamic behavior of the system under foundation excitation and pulsating flow were analyzed. Numerical results showed that the first critical flow velocity of the pipe system has the trend of increasing firstly and then decreasing with increase in elastic coefficient;when elastic coefficient is large enough,the modal-coupling phenomena of the first mode and the second one of the pipe system occur with increase in flow velocity; the system response has the feature of transition from period-doubling bifurcation into chaotic motion with increase in of flow rate; the system response keeps the chaotic motion state under the condition of enough large flow velocity.