The implementation of the nonlinear tuned vibration absorber (NLTVA) for the suppression
of shimmy vibration in towed wheels is addressed in this study. We adopt a modified
straight tangent tyre model of a single-degree-of-freedom towed wheel system with
an attached NLTVA. Stability analysis illustrated that the NLTVA can significantly
improve the stability of the equilibrium of the wheel. Bifurcation analysis highlighted
the existence of large bistable regions, which undermines the system’s safety. However,
numerical continuation analysis, coupled with a dynamical integrity investigation,
revealed that the addition of an intentional softening nonlinearity in the absorber
restoring force characteristic enables the complete suppression of the bistable regions,
also reducing the amplitude of shimmy oscillations in the unstable region. Quasiperiodic
motions were also identified; however, their practical relevance seems marginal.