The nonlinear dynamics of two-wheeled trailers is investigated using a spatial 4-DoF
mechanical model. The non-smooth characteristics of the tire forces caused by the
detachment of the tires from the ground and other geometrical nonlinearities are taken
into account. Beyond the linear stability analysis, the nonlinear vibrations are analyzed
with special attention to the nonlinear coupling between the vertical and lateral
motions of the trailer. The center manifold reduction is performed leading to a normal
form up to third degree terms. The nature of the emerging periodic solutions, and,
thus, the sense of the Hopf bifurcations are verified semi-analytically and numerically.
Simplified models of the trailer are also used in order to point out the practical
relevance of the study. It is shown that the linearly independent pitch motion affects
the sense of the Hopf bifurcations at the linear stability boundary. Namely, the constructed
spatial trailer model provides subcritical bifurcations for higher center of gravity
positions, while the commonly used simplified mechanical models explore the less dangerous
supercritical bifurcations only. Domains of loss of contact of tires are also detected
and shown in the stability charts highlighting the presence of unsafe zones. Experiments
are carried out on a small-scale trailer to validate the theoretical results. A good
agreement can be observed between the measured and numerically determined critical
speeds and vibration amplitudes.
