## 1 Introduction  
The strict regulations for reduced emissions have driven the automotive industry towards developing downsized, turbo-charged engines with higher fuel efficiency. The drawback is the generation of aggressive drivetrain torsional oscillations due to the increased power to weight ratio [1]. A common by-product of drivetrain oscillations that penetrate the transmission is gear rattling noise [2, 3], which is predominantly radiated due to the impacts of the unloaded (non-engaged) gear pairs. To overcome the adverse effects of gear rattling noise on vehicle quality perception, expensive and sizeable palliatures tuned to certain frequency ranges (such as dual-mass flywheels, clutch pre-dampers and centrifugal pendulum absorbers) [4, 5] are employed by automotive manufacturers. Nevertheless, because of the tuning conditions, these palliatures do not act in a broadband manner over the powertrain response. Recent studies [6, 7, 8, 9, 10, 11] have revealed the potential of using nonlinear vibration absorbers (nonlinear energy sinks (NES)) with low mass and inertia properties for effectively attenuating the generation and propagation of powertrain torsional oscillations. The NES possesses essentially nonlinear stiffness and, thus, instead of being tuned to a preferential frequency, it is activated by the energy input. This is the concept of targeted energy transfer (TET) (also known as energy pumping), whereby the oscillatory energy is transferred in a nearly irreversible manner from a primary system donor (drivetrain) to a secondary system receiver (NES) [12], where it is then either redistributed within the modal domain or locally dissipated. Numerous publications in the literature have been dedicated to understanding, designing and optimising NES vibration absorbers by studying the underlying dynamics [13; 14; 15; 16; 17; 18]. The vast majority of works concern absorbers that are acting in translational motion and comprise investigations where an NES was implemented on reduced-order primary system models [13; 14]. The dynamics of energy pumping in systems equipped with an NES have been systematically investigated by parametric studies of the system's main properties [15], whereas studies have considered both grounded and ungrounded NES absorbers [16; 17] to understand their nonlinear dynamics and the NES effectiveness. The activation of nonlinear normal modes (NNMs) has been also discussed [18] to illustrate how the NES may interact with the primary system. More recently, NES mechanisms have been studied for passive structural control purposes and were shown to effectively dissipate energy from structural systems during oscillatory operating conditions. Time-domain numerical methods have been utilised due to the geometric nonlinearities of the NES [9; 19]. An NES with an inerter (NESI) for passive vibration control has been presented [20; 21], converting relative translational motion to rotational motion. The small physical mass of the inerter is an advantage, potentially enabling the NESI to provide comparable vibration attenuation to an NES that possesses a larger physical mass. An alternative NES configuration has been proposed utilising bi-stability (BNES) with buckled beams to suppress the oscillations of unbalanced rotor systems [22]. The numerical simulations have been verified by experimental work to confirm the performance of the BNES. The results showed that the BNES can effectively deal with varied energy quantities. Nevertheless, a limited number of studies involving rotational NES have been reported in the literature. A torsional NES was proposed in [23] to stabilise a rotational drilling system. The dynamics of a rotational NES mounted within a linear oscillator were studied in [24]. The suppression of torsional aeroelastic instabilities on a flexible wing was examined experimentally using a rotational NES that was housed on the tip of the wing [25]. Steel wire was employed as a mechanism for generating cubic force nonlinearity.