Nonlinear dynamics analysis of rotor systems based on extended nonlinear modal theory with gyroscopic coupling

The nonlinear dynamic characteristics of rotor systems exhibit dual dependence on rotor speed and vibration amplitude, a phenomenon originating from the synergistic effects of gyroscopic coupling and inherent nonlinearities such as dry friction. Current research faces two critical challenges: (A) the insufficient characterization of gyroscopic coupling mechanisms in nonlinear modal analysis, particularly for large-scale rotor systems; (B) the lack of efficient methods for predicting critical speeds and unbalance responses in nonlinear regimes. To address these issues, this paper proposes an Extended Nonlinear Mode Synthesis (ENMS) framework with three fundamental innovations: (A) Establishment of a gyroscopic-coupled governing equation incorporating antisymmetric matrix formulation, enabling systematic characterization of speed-dependent nonlinear modes; (B) Development of amplitude-speed correlation models revealing the nonlinear transition mechanisms of modal characteristics; (C) Derivation of an efficient computational scheme for critical speed determination and approximate unbalance response prediction. The proposed methodology demonstrates breakthrough advantages in computational efficiency while maintaining high precision when validated through missile engine rotor case studies. This study establishes a complete theoretical framework for gyroscopic-coupled nonlinear modal analysis, providing a paradigm-shifting tool for complex rotor dynamics design and vibration control.