The nonlinear dynamics of towed wheels is analysed with the help of the brush tyre model. The time delay in the tyre-ground contact and the non-smooth nature of the system caused by contact friction are considered simultaneously. Firstly, the centre manifold reduction is performed on the infinite-dimensional system transforming the governing equations into a normal form containing linear and piecewise-smooth secondorder terms. Then, this normal form is used to establish the stability of the non-hyperbolic equilibria of the system and to give an estimation of the limit cycles emerging at the linear stability boundary. This way, it is demonstrated how subcritical Hopf bifurcations in the non-smooth delayed system generate bistable parameter ranges, which are left undetected by standard tyre models.

In this study a tyre model is developed for multibody dynamics software. Vibrations of a towed wheel excited by the lateral deformation of the tyre are analysed with the help of numerical simulations. In our calculations the time delay in the tyre-ground contact as well as the partial side slip are considered making it possible to capture the dynamic deformation of the contact patch centre-line with relatively low number of parameters and computation time. As a result the hysteresis effect in the stability of the rectilinear motion can be identified, which would be undetectable by simpler, quasi steady-state tyre models. Thus, bistable parameter regions appear in the stability charts where for the same set of system parameters a stable equilibrium and a periodic orbit coexist. The simulations are compared with measurements carried out on an experimental rig consisting of a wheel and a caster running on a conveyor belt. Keywords tyre-road contact • dynamic tyre • deformation • non-smooth delayed tyre model • lateral vibrations • wheel shimmy ACKNOWLEDGEMENT This research has been supported by theÚNKP-17-13-I. New National Excellence Program of the Ministry of Human Capacities.

In this study, we consider the experimentally obtained, periodically forced response of a nonlinear structure in the presence of process noise. Control-based continuation is used to measure both the stable and unstable periodic solutions, while different levels of noise are injected into the system. Using these data, the robustness of the control-based continuation algorithm and its ability to capture the noise-free system response are assessed by identifying the parameters of an associated Duffing-like model. We demonstrate that control-based continuation extracts system information more robustly, in the presence of a high level of noise, than open-loop parameter sweeps and so is a valuable tool for investigating nonlinear structures.

The lateral stability of the car-trailer combination is analysed by means of a single track model. The equations of motion are derived rigorously by means of the Appell-Gibbs equations for constant longitudinal velocity of the vehicle. The tyres are described with the help of the so-called delayed tyre model, which is based on a brush model with pure rolling contact. The lateral forces and aligning torques of the tyre/road interaction are calculated via the exact instantaneous lateral deformations in the contact patches. The linear stability analysis of the rectilinear motion is performed via the analytically determined characteristic function of the system. Stability charts are constructed with respect to the vehicle longitudinal velocity and the payload position on the trailer. Self-excited lateral vibrations are detected with different vibration modes at low and at high longitudinal speeds of the vehicle. The effects of the tyre parameters are also investigated.

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