Decoupling analysis on nonlinear system based on the modified generalized frequency response functions

This paper presents a nonlinear decoupling approach based on the Modified Generalized Frequency Response Functions (MGFRFs) and the nonlinear feature of phase invariance, for the pure nonlinearity-input nonlinear system. The MGFRFs are defined by combining the ‘homotopy’ GFRFs and phase information of the system input. The nonlinear feature of phase invariance is extracted based on MGFRFs. The decoupling approach is proposed based on MGFRFs and extended from the pure tone excitation to the multi-tone excitations by considering phase invariance. Numerical simulation and experimental investigation were carried out, whose results have shown that nonlinear feature of phase invariance is correct and reasonable and the proposed decoupling approach is valid and feasible. The proposed decoupling approach can be employed to identify the excitation sources and to estimate nonlinear system parameters for the pure nonlinearity-input nonlinear vibration system.

• The modified generalized frequency response functions are presented.
• Features of phase invariance are extracted after the MGFRFs are formed.
• A decoupling approach is proposed based on MGFRFs and phase invariance.
• Vibration system that we studied is the pure nonlinearity-input nonlinear system.
• The proposed method is valid of vibration analysis and source identification.