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A generic methodology has been developed to calculate and to perform the global optimization of resonance forced response levels and resonance frequencies for essentially nonlinear vibrations of gas-turbine structures with friction and gap contact interfaces. The methods developed allow effective analysis for large-scale finite element models containing millions degrees of freedom and detailed description of friction contact interfaces in jointed structures. The resonance peak characteristics can be calculated directly as functions of design parameters and excitation. The resonance peak forced response and frequency are calculated in frequency domain using multiharmonic representation of the periodic forced response. Capabilities of the method are demonstrated on examples of analysis of large-scale finite element models of realistic bladed discs with nonlinear contact interfaces: (i) a high pressure bladed disc with shroud contacts and (ii) a bladed disc with friction damping at blade fir-tree roots, The numerical investigations show the high efficiency of the methods developed in the determination of resonance response and frequency dependencies to parameters of friction contact interfaces, and in the search for an optimal set of parameters providing required resonance peak characteristics.