A Nonlinear vibration analysis of forced response for a bladed-disk with dry friction dampers

This paper focuses on the steady vibration characteristics of the bladed-disk subjected to the dry friction damping under periodic excitation. The multi-harmonic method and continuation procedure are combined to trace the solution of the nonlinear forced vibration problem. To obtain a stable and fast nonlinear solver, the analytical formulation of Jacobian matrix in frequency-domain is derived for elastic Coulomb friction model with variable normal force. Furthermore, the continuation method is generalized to trace the solution via different parameters, including not only commonly used excitation frequency but also other design parameters of interest. In numerical simulations, a two degrees of freedom system and a lumped parameter bladed-disk model with dry friction dampers are employed to validate the effectiveness and stability of the method. Meanwhile, the effects of damper design parameters on the responses are investigated, especially the effect of normal force is studied to find the optimal solution. The results indicate that the proposed analytical method can provide an accurate quantitative assessment for the optimum design of the bladed-disk dampers.