Tuned pendulum as nonlinear energy sink for broad energy range

Nonlinear energy sinks (NES) are widely studied as a possible engineering solution for mitigation of steady-state, impulsive and transient broadband excitations. Current work is devoted to the applicability of common pendulum as the NES for mitigation of impulsive excitations. It turns out that the pendulum NES can overcome one of the main shortcomings of more traditional NES designs, since it is able to mitigate excitation of a primary system in a relatively wide range of initial energies. This is because the pendulum can be captured into a resonance with primary oscillator both for rotational and oscillatory responses. If parameters are chosen properly, for small energies the pendulum responds almost as a common tuned mass damper. However, at higher energies, the pendulum acts as rotational NES. Thus, relatively broad diapason of initial energies can be covered. This paper presents numeric evidence for the efficiency of this design of the NES and discusses its optimal tuning. Another important finding is that the NES's efficiency exhibits rather broad deviations for different realizations of the initial conditions with the same energy. We present a theoretical analysis of the damped targeted energy transfer into the pendulum NES from the primary mass with an account of corrections caused by the effect of gravity.