Finite contact duration modeling of a Vibro-Impact Nonlinear Energy Sink to protect a civil engineering frame structure against seismic events

This paper reassesses carefully the effects and consequences of instantaneous contact mechanics versus finite contact duration modeling of Vibro-Impact Nonlinear Energy Sinks (VI NES). The device is composed of a container enclosing an inelastic sphere, interacting via a nonlinear viscoelastic dissipative force with the inner walls of the container. The VI NES is considered in a practical context, the control of the vibrations of a civil engineering frame structure under seismic input. It is connected by a rigid link to the structure: the particle bounces within the container when it vibrates, exploring dynamical regimes ranging from periodic collisions to chaos while dissipating energy. Our VI NES is designed in order to mitigate vibrations of a ten-story frame structure under two historic earthquake signals, in order to rule out specific effects. The dynamics of the system, obtained from both finite and instantaneous contact models, are compared and discussed. The main result reveals a significant effect of the contact duration on the estimation of the dissipated energy, even for very brief collisions. Instantaneous contact model indeed provides incommensurate values in terms of acceleration during the impacts, leading to a higher sensitivity to Initial Conditions (IC) revealed by large fluctuations of the mechanical response. In turn, any finite duration contact models is proved to be less sensitive to IC, and thus more precise. Our findings demonstrate that both finite and instantaneous models converge in fact to the same value, in average, but the finite duration models require much less realizations to converge to the mean value. In practice, the finite contact duration low pass filters the mechanical responses of the VI NES, avoiding the system to fall into nonphysical chaotic states experienced by the instantaneous model.