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 a first time, this capability for analysis of strongly nonlinear periodic vibrations of bladed discs 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, normal stresses. High accuracy and efficiency of the new method have been demonstrated on numerical examples including large-scale nonlinear bladed disc model and major types of contact interfaces including friction contact interfaces, gaps and cubic nonlinearities.
