High dimensional nonlinear spring characteristic modelling and vibration analyses of subharmonic resonance of a dual-rotor system based on energy tracks

Abstract

The subharmonic resonance is a typical nonlinear vibration that occurs in a nonlinear rotor system. In this paper, expressions of the potential energy of rotor systems are derived systematically, and the high dimensional nonlinear spring characteristic modelling is revealed firstly through the potential energy with nonlinear variation characteristics. A novel nonlinear dual-rotor model considering nonlinear spring characteristics is proposed to reveal the inducing mechanism of subharmonic resonances of rotors and to study vibration characteristics of subharmonic resonances of the dual-rotor system. The new concepts such as energy tracks, the energy-phase plane and energy-spectrum analyses are presented to analyze nonlinear variation characteristics of the potential energy of rotors, and results show that different nonlinear coefficients correspond to subharmonic resonances of different orders, respectively. The resonance responses in the vicinities of critical speeds of subharmonic resonances of orders 1/2 and 1/3 to be obtained by numerical simulations and theoretical analyses are discussed comprehensively. It is found that a group of independent branching solutions in the solution space appears corresponding to subharmonic resonances in the vicinity of coupling subharmonic critical speeds. In addition, analysis results of numerical simulations based on energy concepts are consistent with results of theoretical analyses about the potential energy of rotors. This study is beneficial to understand the inducing mechanism of subharmonic resonances of rotors, and verifies the correctness of the high dimensional nonlinear spring characteristic modelling and the proposed nonlinear dynamic model of the dual-rotor system.