Constant-excitation caused response in a class of parametrically excited systems with two degrees of freedom

Abstract

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.