Identification by means of a genetic algorithm of nonlinear damping and stiffness of continuous structures subjected to large-amplitude vibrations. Part I: single-degree-of-freedom responses

A procedure is presented to identify the nonlinear damping and stiffness parameters of a single-degree-of-freedom (SDOF) model from large-amplitude vibrations of harmonically forced continuous systems, in absence of internal resonances. Cubic nonlinear damping is introduced in the SDOF model in addition to the classical viscous one. The parameter estimation relies on the harmonic balance method. It is shown that the mean value, the first and the second harmonics are needed for a softening response, although often only the first harmonic is experimentally measured with accuracy. The identification methodology is thus split between (i) purely hardening and (ii) softening behaviour. The absence of coupling enables for an independent estimation of the nonlinear stiffness from the backbone curve, followed by an evaluation of damping at resonance. For the purely hardening case, the classical least-squares method is applied by using experimentally measured first harmonic. For the softening case, a 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 two-term harmonic balance model by means of a genetic algorithm. These procedures are validated by parameter identification on synthetic (numerically generated) and experimental frequency-responses. In particular, the identified nonlinear damping model is compared to level-adjusted linear viscous damping with a different coefficient identified at any level of harmonic force, demonstrating its ability to account for the evolution of damping with the vibration amplitude. The identification of one-to-one internal resonances is treated in a companion paper.