外激励作用下输流管道伴随内共振的非线性振动分析

摘要

An external periodic load was considered to act on a fluid-conveying pipe clamped at both ends,and the nonlinear forced vibration of such a system was 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 nearly at the middle of first two natural frequencies,accompanied internal resonance may occur to form a combination resonance.The characteristics of the response were discussed,and the motions of first two modes were investigated in detail.The influence of excitation amplitude on the internal resonance was analyzed.Some numerical examples reveal the rich and complex dynamic behaviors caused by internal resonance and show that the occurrence tendency of internal resonance will die down and the response modes will vary with the increase of excitation amplitude. The convenience and efficiency of the MDLP method in predicting nonlinear dynamics are demonstrated by the results of the study.%利用多元 L -P 法研究外部周期激励下两端固定输流管道伴随内共振的非线性受迫振动问题。外激励流固耦合系统固有频率第二阶约为第一阶3倍且激励频率接近前两阶固有频率中间值时会发生伴随强烈内部共振的组合共振，并用多元 L -P 法求解振动响应，分析前两模态运动及外激励幅值对内共振的影响。数值算例揭示出系统因内共振发生的更丰富、复杂的动力学行为，随激励幅值增大内共振发生趋势降低，响应形式亦发生变化。用多元 L -P 法研究非线性动力学便捷、高效。