一类两自由度参激系统在常数激励下的响应研究*

摘要

本文探讨常数激励对参激系统共振响应的影响。以机动飞行的裂纹转子系统为例，建立一个两自由度的振动方程，其中裂纹的呼吸行为构成参数激励，机动飞行引起的机动载荷简化为常数激励，并假设转子为平衡转子，不考虑偏心激励的影响。采用谐波平衡法求解振动方程，得到各次谐波响应与转速及常数激励的关系式，从而分析系统的共振响应。结果表明，常数激励对系统的参激主共振及超谐共振响应起决定性作用，这符合普通裂纹转子系统的重力占优理论，同时，系统各次谐波响应的幅值随常数激励的增加而增大，常数激励的作用方向对参激主共振响应的幅值影响较大，但对参激超谐共振响应的幅值影响很小。这说明常数激励能起到放大裂纹转子系统超谐共振响应的作用，不利于系统的平稳运行，但从另一角度考虑，常数激励可用于裂纹故障的早期检测。%This paper focuses on the response in parametrically excited systems caused by constant excitation. Taking a maneuvering cracked rotor system as an example, we formulate the vibration equations with two degrees of freedom, in which the breathing of the crack constitutes parametric excitation, and the maneuver load of the maneuvering rotor is simplified as a constant excitation, and it is supposed that the rotor system is balanced without the consideration of eccentricity. By solving the equations with harmonic balance method, each order of harmonic components related with the rotating speed and the constant excitation is derived to analyze the corresponding resonance of the system. Results show that the constant excitation plays a decisive role in the parametrically excited primary and super-harmonic resonances of the system that agrees with the gravity dominance in common cracked rotor systems without maneuver load. And the stronger the constant excitation, the greater the resonances. Moreover, the orientation of the constant excitation makes a great impact on the parametrically excited primary resonance, but does not have a significant effect on the parametrically excited super-harmonic resonances. Results implies that constant excitation may increase the parametrically excited super-harmonic resonances of the cracked rotor systems, which is disadvantageous to the operating of the system. From another point of view, however, constant excitation can be used for early detection of crack faults in rotor systems.