Wheel shimmy suppression through the piecewise nonlinear energy sink: elimination of detrimental isolas

Several researchers have investigated shimmy suppression using Tuned Mass Dampers (TMD) and cubic Nonlinear Energy Sink (C-NES) in common solutions. These devices are typically mounted on the wheel frame. The wheel system equipped with the vibration absorber is derived from the integration of the single wheel system model and the governing equations of the vibration absorber. As a result, we have assessed the linear stabilities of both the TMD and C-NES, as illustrated in the first figure.

While the TMD clearly enhances the linear stability of the system, the C-NES has a comparatively lesser impact on linear stability. In the accompanying figure, I also present both the Generalized Mass Damper (GMD) and the Cubic Energy Sink (CES). For a specific system represented by the red dot in the figure, the mechanisms of stabilization differ between TMD and C-NES. The TMD achieves stabilization by modifying the zero attractor stability, while the C-NES operates through a different mechanism.