密集模态组间非线性相互作用的初步研究

 基于平均 Lagrange函数与调制项关系的 ALFM法,研究了通过 2∶ 1内共振联系的密集模态组间复杂的非线性相互偶合作用,深入探讨了密频内共振与 2∶ 1内共振的关系,提出了密集模态组在低阶主共振条件下相互作用及整体表现的初步规律,对于具有密集模态的大型柔性航空航天结构的振动主动控制和模态分析研究具有重要的指导意义

STUDY ON THE NONLINERAR INTERACTION BETWEEN THE GROUPS OF MODELS WITH CLOSELY SPACED NATURAL FREQUENCIES

Firstly, based on the relationship between the Average Lagrangian Function(A.L.F) and amplitude phase modulations, the system average equations were derived in another way which is different from the classical average method. And then the amplitude frequency equation was derived from the system amplitude phase modulations, the Newton numerical iteration was used to resolve the amplitude frequency equation, and the complicated nonlinear interaction between the gruops of models with closely spaced natural frequencies connected with 2∶1 internal resonance was discussed. Secondly, by investigating the relationship between 1∶1 internal resonance and 2∶1 internal resonance, the basic rule of the nonlinear interaction and its exhibiting as a whole in the groups of models with closely spaced natural frequencies was put forward. The conclusions reached here are very important to the active vibration control and modal analysis to the large flexible aeronautics and astronautics structures with closely spaced natural frequencies.