Response regimes of a linear oscillator with a nonlinear energy sink involving an active damper with delay

In this paper, we consider a linear oscillator subject to periodic excitation coupled to a nonlinear energy sink with piecewise-quadratic damping characteristics. The damping model includes a time delay to take into account the time needed to change the damping characteristics. In the framework of singular perturbation theory, an analytical/numerical procedure combining complexification, averaging, and multiple scale approaches is used to predict period and quasiperiodic response regimes. The analytical predictions agree satisfactorily with numerical results. It is shown that introducing a relatively small time delay causes significant modifications in the system regimes including suppression of quasiperiodic response regimes and reduction of the response level.