<p>Recent developments in wheel shimmy suppression have demonstrated the effectiveness of nonlinear energy sinks (NESs) in absorbing vibrational energy and reducing the amplitude of shimmy oscillations. Shimmy mitigation relies on strongly modulated responses (SMR), which exhibit significantly lower amplitude compared to the uncontrolled system. However, previous studies have shown the coexistence of a high-amplitude isolated branch of periodic solutions, which limits the global stability of the SMR and undermines the effectiveness of the NES. To address this issue – and building upon state-of-the-art NES designs – this paper proposes a novel approach to ensure the effectiveness of NESs in mitigating the shimmy of a towed wheel. In particular, the NES is augmented with a piecewise linear damping characteristic, which does not compromise its original performance but effectively eliminates the detrimental branch of isolated responses, making the SMR globally stable. First, a multiple-scale analysis is employed to analytically identify the sources of shimmy excitation. Then, a detailed comparison between the NES and a tuned mass damper highlights the NES’s advantages in terms of robustness against parametric perturbations. Based on these findings, a piecewise damping design is incorporated into the optimized cubic NES structure. By examining the global bifurcation diagram and performing subsequent parametric optimization, the detrimental isola is successfully eliminated while preserving the desired SMR branch. Finally, the robustness of NES parameters against real-world manufacturing errors is evaluated, demonstrating the practical feasibility of the proposed approach for shimmy control in various types of wheeled vehicles.</p>