悬臂输流管道在基础激励与脉动内流联合作用下的参激振动

首先建立了悬臂输流管道在基础激励与脉动内流联合作用下的运动方程;然后基于Galerkin法研究了该系统的非线性动力学行为,分析了系统运动状态随激励频率和相位差的变化,以及混沌百分比随频率比(基础激励频率与脉动频率之比)和相位差的变化。结果表明,无论以激励频率还是以相位差为分岔参数,系统都具有多种形式的动态响应,包括周期运动、概周期运动和混沌运动,但进入和脱离混沌的途径不同。相位差和频率比对系统的混沌百分比有重要影响:相位差为π/2时系统混沌百分比最大;频率比为1时系统混沌百分比最小,频率比较小或较大时系统混沌百分比与只有基础激励时接近。

Parametric vibration of cantilevered pipes under combined action of foundation excitation and pulsating internal flow

The equations of motion of cantilevered fluid-conveying pipes with the co-action of foundation excitation and pulsating flow are established.Nonlinear dynamic behaviors of the system are studied by using theGalerkin method.Variation of motion state of the system with excitation frequency and phase difference and variation of chaotic percentage with frequency ratio and phase difference are analyzed.Results show that the system has a variety of dynamic responses,including periodic,quasi-periodic and chaotic motion,with either excitation frequency or phase difference as the bifurcation parameter,but routes approaching and leaving chaotic motions are different.Phase difference and frequency ratio have important influences on chaotic percentage of the system.If phase difference isπ/2,chaotic percentage of the system has its maximum.If frequency ratio is 1,chaotic percentage of system has its minimum,and if frequency ratio is very small or very large,chaotic percentage of system is close to that with only foundation excitation.