具有非线性运动约束输液曲管振动的分岔

VIBRATION BIFURCATIONS OF A CURVED PIPE CONVEYING FLUID WITH NONLINEAR CONSTRAINT

研究了具有非线性运动约束输液曲管在系统参数区域内振动的分岔现象。基于牛顿法推导出了输液曲管模型面内振动的非线性控制方程,利用微分求积法将系统的偏微分方程转化为关于时间域的二阶常微分方程组;在此基础之上,采用数值迭代技术求解了输液曲管的非线性动力学方程。数值模拟表明,输液曲管在系统多种参数区域内存有复杂的分岔现象;在这些参数区域内,系统将以静态变形、周期运动和混沌等形式作复杂的振动。

The nonlinear partial-differential equation governing in-plane vibration of a curved pipe is derived via Newtonian method.The differential quadrature method(DQM) is applied to truncate the governing equation into a set of two-order ordinary differential equations with respect to time domain.Calculations of bifurcation diagrams of the oscillation demonstrate the definitive existence of complex bifurcations in the parameter spaces.From numerical simulations,it is(indicated) that the static deformation,periodic and chaotic motions occur in the vibrations of the curved pipe conveying(fluid).The results are useful for the designers to check the vibration and stability of piping systems.