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The present analysis deals with the ground taxiing of aircrafts and considers, in particular, their turning at rather low speed with very small path radii among obstacles that may be very close to each other, for example inside the hangars or on the flight decks of the aircraft carriers where other planes stand stationary. To succeed in this operation, it is crucial to optimize the path and avoid dangerous collisions or, more generally, the interference in the ground projection between the obstacles and the band enclosing all the point trajectories of the plane. The essential innovation here proposed for this purpose consists in making all the wheels of the undercarriage steerable, assuming electrically motorized struts, and in searching for the best correlation among the steering angles in order to optimize the path. The geometrical and dynamical nonlinearities due to the relatively large steering angles, to the changes of the cornering stiffness with the vertical loads on the wheels and to the inertial and the aerodynamic forces will be included in the analysis. The rollover critical speeds will be calculated on varying the path radius.

Comparing with the tractor-trailer systems for the road haulage, which must cope with some typical undesired trends, such as high-speed instability, over- or under-steering and off-tracking, the multi-trailer systems for the transport of luggage in the airports or in the railway stations, or for the transfer of goods in the warehouses, run at quite low speeds, but must manage to steer clear of the many obstacles encountered along their path. This type of vehicle is not subject to tire cornering phenomena, because the speed is just low and the wheels are generally stiff. Hence, the vehicle movement is in practice ruled by the non-holonomic rolling constraint of the wheels and by the steering device mounted on the trailers, which may consist in drawbars integrated with the front axles and rotating around a central pin (dolly-semitrailer systems), or else in roulettes set back with respect to their vertical connection pins to the trailer chassis (caster-trailer systems). The present analysis addresses all the interconnected aspects of the mechanical behaviour of these types of multi-trailer systems in an organic whole, starting from the kinematical analysis of the possible paths and their stability, giving guidelines for the proper layout of the vehicle units to eliminate the steady off-track, and ending with the calculation of the traction forces through the various links and the road forces at the ground prints, in order to gain information useful to check the stress state of the various structural elements.

The two main sources of internal friction in a rotor-shaft system are the shaft structural hysteresis and the possible shrink-fit release of the assembly. The internal friction tends to destabilize the over-critical rotor running, but a remedy against this effect may be provided by a proper combination of some external damping in the supports and an anisotropic arrangement of the support stiffness, or at most by the support damping alone, depending on the system geometry. The present analysis reported here considers a general asymmetric rotor-shaft system, where the rotor is perfectly rigid and is constrained by viscous–flexible supports having different stiffnesses on two orthogonal planes. The internal friction is modelled by nonlinear Coulombian forces, which counteract the translational motion of the rotor relative to a frame rotating with the shaft ends. The nonlinear equations of motion are dealt with using an averaging approach based on the Krylov-Bogoliubov method with some adaptation to address the multi-degree-of-freedom nature of the problem. Stable limit cycles may be attained by the overcritical whirling motions, whose amplitudes are inversely proportional to the external dissipation applied by the supports. A noteworthy result is that the stiffness anisotropy of the supports is recognized as beneficial in reducing the natural whirl amplitudes, albeit mainly in the symmetric configuration of the rotor at the mid span and, to a rather lesser extent, in the asymmetric configuration, which then requires a stronger damping action in the supports.