General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Considering the desirable case where no shimmy occurs we define the set of allowable freeplay profiles that satisfy a conservative stability criteria.

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. Abstract.Commercial aircraft are designed to fly but also need to operate safely and efficiently as vehicles on the ground. During taxiing, take-off, and landing the landing gear must operate reliably over a wide range of forward velocities and vertical loads. Specifically, it must maintain straight rolling under a wide variety of operating conditions. It is well known, however, that under certain conditions the wheels of the landing gear may display unwanted oscillations, referred to as shimmy oscillations, during ground maneuvers. Such oscillations are highly unwanted from a safety and a ride-comfort perspective. In this paper we conduct a study into the occurrence of shimmy oscillations in a main landing gear (MLG) of a typical midsize passenger aircraft. Such a gear is characterized by a main strut attached to the wing spar with a side-stay that connects the main strut to an attachment point closer to the fuselage center line. Nonlinear equations of motion are developed for the specific case of a two-wheeled MLG configuration and allow for large angle deflections within the geometrical framework of the system. The dynamics of the MLG are expressed in terms of three degrees of freedom: torsional motion, in-plane motion, and out-of-plane motion (with respect to the side-stay plane). These are modeled by oscillators that are coupled directly through the geometric configuration of the system as well as through the tire/ground interface, which is modeled here by the von Schlippe stretched string approximation of the tire dynamics. The mathematical model is fully parameterized and parameters are chosen to represent a generic (rather than a specific) landing gear. In particular, the positions of the attachment points are fully parameterized so that any orientation of the side-stay plane can be considered. The occurrence of shimmy oscillations is studied by means of a two-parameter bifurcation analysis of the system in terms of the forward velocity of the aircraft and the vertical force acting on the gear. 1. Introduction. The technical term shimmy is generally used to describe the self-sustained oscillations of a system with one or more rolling wheels and represents a relatively well-studied problem in engineering. Typical examples of shimmy with which the reader may be familiar range from the weaving of a towed trailer at high speeds to the sudden oscillation of a loose trolley wheel. The phenomenon first began to attract research interest in connection with the undesirable oscillation of the steering mechanism of early automobiles. These vehicles shared the common design elements of a single front axle rigidly connected to the front wheels, and the severity of the problem increased further with the development...

This paper details five aeroelastic modelling methods applied to the study of an example high aspect ratio wing subject to high loads resulting in large structural deformations. Each method is discussed in turn and example static results from each are compared. Overall agreement is illustrated between the methods for key quantities of interest although aerodynamic modelling choices regarding the orientation of aero forces is observed to play a significant role in the agreement between predicted distributed loads and deflections. Quantitative differences resulting from linearisation of the wing model are also presented and discussed. It is found that by linearising the problem, wing deflection, aerodynamic forces and root bending are all over-estimated. Large differences are also observed between linear and nonlinear predictions of root twist, however the modelling of drag effects is deemed important to the exact nature of the observed discrepancy. Altogether, linearised assumptions are shown to have a noticeable impact on the accuracy of predicted results for the considered wing test case and are deemed unsuitable in isolation for the analysis of this class of flexible problem.

This paper proposes a low-order geometrically exact flexible beam formulation based on the utilization of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam shapes approach is in contrast to the majority of geometrically nonlinear treatments in the literature in which element-based—and hence high-order—discretizations are adopted. The kinematic quantities approximated specifically pertain to shear and extensional gradients as well as local orientation parameters based on an arbitrary set of globally referenced attitude parameters. In developing the dynamic equations of motion, an Euler angle parametrization is selected as it is found to yield fast computational performance. The resulting dynamic formulation is closed using an example shape function set satisfying the single generic kinematic constraint. The formulation is demonstrated via its application to the modelling of a series of static and dynamic test cases of both simple and non-prismatic structures; the simulated results are verified using MSC Nastran and an element-based intrinsic beam formulation. Through these examples, it is shown that the nonlinear beam shapes approach is able to accurately capture the beam behaviour with a very minimal number of system states.

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