A numerical method for calculating nonlinear resonance response surface based on nonlinear modes

Excessive vibration causes high cycle fatigue and seriously threatens the integrity of mechanical structures, especially when resonance occurs. The existence of nonlinearities such as large deformation and dry friction, makes it time consuming to predict the resonance response during parameter studies. In this paper, a numerical method is proposed for efficiently predicting the resonance response surface of nonlinear systems based on nonlinear modes. The resonance response surface is defined as the hypersurface formed by the resonance peaks under different combinations of excitation levels and nonlinear parameter values in this paper. The nonlinear modal analysis is carried out only once to obtain the resonance response surface. There are two core steps of this method. First, by using the extended energy balance method, we establish the relationship between the excitation force and the resonance amplitude. Next, the mapping between the nonlinear parameter value, the excitation level, and the resonance amplitude is analytically derived. A one-DoF Duffing vibrator and a lumped parameter model containing dry friction are tested to verify this method. High accuracy and efficiency have been proved. Compared with the steady-state response analyses, the maximum relative error is less than 0.1%.