Direct Parametric Analysis of Resonance Regimes for Nonlinear Vibrations of Bladed Disks

A method has been developed to calculate directly resonance frequencies and resonance amplitudes as functions of design parameters or as a function of excitation levels. The method provides, for the first time, this capability for analysis of strongly nonlinear periodic vibrations of bladed disks and other structures with nonlinear interaction at contact interfaces. A criterion for determination of major, sub-, and superharmonic resonance peaks has been formulated. Analytical expressions have been derived for accurate evaluation of the criterion and for tracing resonance regimes as function of such contact interface parameters as gap and interference values, friction and contact stiffness coefficients, and normal stresses. High accuracy and efficiency of the new method have been demonstrated on numerical examples including a large-scale nonlinear bladed disk model and major types of contact interfaces including friction contact interfaces, gaps, and cubic nonlinearities.