Identification by means of a genetic algorithm of nonlinear damping and stiffness of continuous structures subjected to large-amplitude vibrations. Part II: one-to-one internal resonances

A procedure is presented to identify the nonlinear damping and stiffness parameters of harmonically forced continuous systems showing nonlinear vibrations with a one-to-one internal resonance. The identification is obtained by using a two-degree-of-freedom (2DOF) model. Cubic nonlinear damping is introduced in the 2DOF model in addition to the classical viscous one. Different damping coefficients are considered within or outside the internal resonance frequency range. The parameter estimation relies on the harmonic balance method. It is shown that a three-harmonic expansion is needed to obtain a converged solution, although often only the first harmonic, without mean component, is experimentally measured with accuracy. The proposed novel cascade procedure consists in (i) a single-term harmonic balance parameter estimation used as initiation of (ii) a minimization of the distance between data and a three-term harmonic balance model by means of a genetic algorithm. These procedures are validated by parameter identification on synthetic (numerically generated) and experimentally measured frequency–responses. The nonlinear damping model is validated by comparison with level-adjusted linear damping model estimated at each level of harmonic force, demonstrating its ability to account for the evolution of damping with the vibration amplitude for different branches of solutions.