Identification of the model parameters based on the ambiguous branches of resonance response curves

Abstract

A concept of the method of determining the parameters describing the damping and the nonlinearity, which can be of physical or geometrical nature, is presented in the paper. The main idea is explained regarding mechanical systems with one degree of freedom, however, the method can be also employed to identification for systems with two DoF provided that the couplings are weak and the resonances do not occur simultaneously. The analysis of stationary resonance states can be reduced only then to the third-degree equation, which is a necessary condition for the applicability of this method. Numerical simulations, which are carried out, confirm the usefulness and accuracy of the method.