Vibration analysis and control method of internal resonant nonlinear system based on coupled nonlinear mode approach

Nonlinearity in vibrating systems can lead to complex vibration phenomena such as internal resonance and mode coupling, significantly influencing dynamic behavior. For better vibration suppression effect, the analysis of vibration characteristics of nonlinear structures and their vibration control methods is of great academic value and engineering significance. This paper proposes a coupled nonlinear mode strategy based on the integration of normal form theory and nonlinear complex mode theory, enabling the characterization of internal resonance in nonlinear systems. The method resolves modal interactions and response features in systems exhibiting internal resonance. Nonlinear modal parameters are extracted to investigate coupling mechanisms between internally resonant modes, with emphasis on energy transfer phenomena across these modes. Vibration control strategies for nonlinear systems with internal resonance are further explored using modal space control techniques. Numerical simulations validate the efficacy of the proposed vibration analysis and control methods. Additionally, a nonlinear modal confidence criterion is introduced to elucidate vibration transmission mechanisms between coupled modes in internally resonant systems. The application of the proposed strategy demonstrates robust vibration suppression across diverse conditions, highlighting its potential for controlling nonlinear structures.