Tuning of vibro-impact nonlinear energy sinks under changing structural parameters. Part 1

This paper studies the efficiency of vibro-impact nonlinear energy sink, that is, vibro-impact damper, in mitigating the primary structure vibrations, i.e., in reducing its total mechanical energy. The primary structure is a linear oscillator that forms a strongly nonlinear vibro-impact system when a vibro-impact damper is coupled to it. When the damper is tuned to a certain value of a structural parameter, in particular, the primary structure damping, its sufficiently high efficiency is maintained in some this parameter range and deteriorates in a wider range. Then tuning the damper design to the appropriate value of the primary structure damping allows to significantly improve its efficiency. Optimization procedures are carried out by the tools of standard software Matlab. However, the optimized parameters of the low-mass damper acquire unusual “strange” values, namely, very large clearance and small damping coefficient. In addition, the areas of bilateral damper impacts both directly on the primary structure and on the obstacle are narrow; the areas of unilateral direct damper impacts on the primary structure are wider. These phenomena, observed in our previous works for one particular value of the primary structure damping, persist for its different values. It is also shown how a VI NES attachment can replace the additional PS damping. The system dynamics with the single-sided vibro-impact nonlinear energy sink coupled to the primary structure is always complex; the amplitude-modulated responses are often occur. The characteristics of such a regime are shown, namely, the time history of displacements with upper envelope, left and right contact forces, the phase portraits with Poincaré maps, and Fourier spectra. Modeling the impact using the nonlinear Hertz’s contact force in accordance with his quasi-static theory allows us to calculate the impact contact forces, take into account and optimize the characteristics of the colliding surfaces. Qualitative figures and tables accompany a large volume of numerical experiments.