非线性弹性地基上悬臂管道的参数振动  

Parametric vibration of a cantilevered pipe conveying pulsating fluid on a nonlinear elastic foundation

作　　者：李云东[1,2] 杨翊仁[2] 文华斌[3] 

机构地区：[1]四川理工学院理学院,四川自贡643000 [2]西南交通大学力学与工程学院,成都613001 [3]四川理工学院机械工程学院,四川自贡643000

出　　处：《振动与冲击》2016年第24期14-18,38,共6页Journal of Vibration and Shock

基　　金：四川省科技厅(2013TD004);四川理工学院校基金(2015KY02)

摘　　要：首先建立了非线性弹性地基上悬臂输流管在振荡流作用下的运动方程,应用Galerkin方法将运动控制偏微分方程离散成常微分方程组。采用数值方法着重讨论了平均流速、脉动幅值、脉动频率和地基剪切刚度等参数对系统动力学行为的影响。结果表明:以平均流速为分岔参数系统会出现拟周期运动,然后是周期运动,接着出现混沌运动;以脉动幅值为分岔参数系统发生周期2,周期4,周期8,然后进入混沌运动;以脉动频率为分岔参数系统先发生拟周期运动,然后在二阶次谐波附近发生混沌运动。另外,地基剪切刚度对系统地周期运动和混沌有抑制作用,随着剪切刚度增大,系统从混沌状态演化到周期状态,直至稳态。The motion equation of a cantilevered pipe conveying pulsating fluid on a nonlinear el-astic foundation was constructed,and was discretized into ordinary differential equations by the Galerkin method. The effect of parameters including mean flow velocity,fluctuation amplitude,fluctuation frequency and shear stiffness on the nonlinear behavior of the system was investigated by a numerical method. The results show that the system can present quasi periodic motion,periodic motion,and chaotic motion if the mean flow velocity is used as the bifurcation parameter; the system presents the period-2,period-4,period-8,and chaotic motion if the fluctuation amplitude is used as the bifurcation parameter; the system firstly shows quasi-periodic motion,then chaotic motion nearby second sub harmonic if the fluctuation frequency is used as bifurcation parameter. Furthermore,foundation shear stiffness can suppress the period motion and chaotic motion of the system. With shear stiffness increasing,chaos state of the system gradually changes into periodic motion until a stable state is obtained.

关 键 词：悬臂输流管 弹性地基 周期运动 混沌运动 

分 类 号：O322[理学—一般力学与力学基础]