输流管道含有内共振的横向受迫振动研究

TRANSVERSE FORCED VIBRATION WITH INTERNAL RESONANCE OF A PIPE CONVEYING FLUID

利用多元L-P法研究外部周期激励下两端铰支输流管道含有内共振的非线性受迫振动问题。对于外激励作用下的流固耦合系统,当第二阶固有频率约为第一阶值的3倍,并且激励频率接近系统固有频率时,系统会发生含有强烈内部共振的主共振。利用多元L-P法求解这种振动响应,并详细分析振动中前两个模态的运动及外激励幅值对内共振的影响。数值算例揭示了系统由于内共振而发生的更加丰富而复杂的动力学行为,并且表明,随着激励幅值的增大,部分内共振的发生趋势将降低并最终消失。研究结果同时证明了多元L-P法在研究非线性动力学方面是便捷而高效的。

An external periodic load is applied on a pinned-pinned pipe conveying fluid, and the nonlinear forced vibration for this system is explored by the multidimensional Lindstedt-Poincaré(MDLP) method. According to the analysis, when the second natural frequency of the system is nearly thrice the first one, and the excitation frequency is near the natural frequencies, a principal resonance with intense internal resonance may occur. The characteristics of responses for the first two modes are investigated in detail. Numerical examples reveal the rich and complex dynamic behaviors caused by an internal resonance. The influence of excitation amplitude on the internal resonance is analyzed and it is shown that some internal resonances of the system will decline and even disappear as the excitation amplitude increases. The convenience and efficiency of the MDLP method in researching nonlinear dynamics are also demonstrated.