Tailoring of pinched hysteresis for nonlinear vibration absorption via asymptotic analysis

• Published in: International journal of non-linear mechanics 2017-09, Vol.94, p.59-71
• Main Authors: Casalotti, A., Lacarbonara, W.
• Format: Article
• Language: English
• Subjects: Absorbers; Algorithms; Asymptotic methods; Asymptotic properties; Dynamic response; Evolutionary algorithms; Frequency response; Hysteresis; Mathematical models; Method of multiple scales; Multiscale analysis; Nonlinear passive control; Nonlinear response; Numerical analysis; Optimization; Parameter sensitivity; Pinching; Sensitivity analysis; Stability analysis; Studies; Vibration absorber; Vibration analysis
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2017.02.015

The method of multiple scales is adopted to investigate the dynamic response of a nonlinear Vibration Absorber (VA) whose constitutive behavior is governed by hysteresis with pinching. The asymptotic analysis is first devoted to study the response of the absorber to harmonic excitations and to evaluate its sensitivity to the main constitutive parameters. The frequency response obtained in closed form allows to carry out the stability analysis together with a parametric study leading to behavior charts characterizing multi-valued softening/hardening responses or single-valued, quasi-linear responses. A two-degree-of-freedom model of a primary nonlinear structure endowed with the hysteretic vibration absorber is investigated to explore transfers of energy from the structure to the absorber resulting into optimal vibration amplitude reduction. The asymptotic solution is proved to be in good agreement with the numerical solution obtained via continuation. The asymptotic approach is embedded into a differential evolutionary algorithm to obtain a multi-parameter optimization procedure by which the optimal hysteresis parameters are found. •The effects of hysteresis with pinching in a vibration absorber are investigated.•The absorber is connected with a hardening nonlinear primary structure.•The dynamic response is found in closed form by the method of multiple scales.•The stability, bifurcations and behavior charts of the absorber are determined in closed form.•The asymptotic solution is employed in a differential evolutionary optimization algorithm.