Impulsive vibration mitigation through a nonlinear tuned vibration absorber

The dynamics of a nonlinear passive vibration absorber conceived to mitigate vibrations of a nonlinear host structure is considered in this paper. The system under study is composed of a primary system, consisting of an undamped nonlinear oscillator of Duffing type, and a nonlinear dynamic vibration absorber, denominated nonlinear tuned vibration absorber (NLTVA). The NLTVA consists of a small mass, attached to the host structure through a linear damper, a linear and a cubic spring. The host structure is subject to free vibrations and the performance of the NLTVA is evaluated with respect to the minimal time required to dissipate a specific amount of the mechanical energy of the system. In order to characterize the dynamics of the system, a combination of numerical and analytical techniques is implemented. In particular, on the basis of the first-order reduced model, slow invariant manifolds of the transient dynamics are identified, which enable to estimate the absorber performance. Results illustrate that two different dynamical paths exist and the system can undergo either of them, depending on the initial conditions and on the value of the absorber nonlinear stiffness coefficient. One path leads to a very fast vibration mitigation, and therefore to a favorable behavior, while the other one causes a very slow energy dissipation.