CAJ | 학술논문

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。
이용다원 L -P 법연구외부주기격려하량단고정수류관도반수내공진적비선성수박진동문제。외격려류고우합계통고유빈솔제이계약위제일계3배차격려빈솔접근전량계고유빈솔중간치시회발생반수강렬내부공진적조합공진，병용다원 L -P 법구해진동향응，분석전량모태운동급외격려폭치대내공진적영향。수치산례게시출계통인내공진발생적경봉부、복잡적동역학행위，수격려폭치증대내공진발생추세강저，향응형식역발생변화。용다원 L -P 법연구비선성동역학편첩、고효。
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.