Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates

The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates (BEC) by solving the Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii (TDGP) equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both the BdG and TDGP approaches allows one to unambiguously identify every observed mode.Comment: 5 pages, 4 figure

Experimental Effect of Sideslip Angle on the Dynamic Behaviour of Flared Folding Wingtips

A concept of growing interest in recent years is the Flared Folding Wingtip (FFWT), which can be used in-flight to reduce airframe loading due to gust encounters and augment the handling qualities of an aircraft. The performance of an FFWT is affected by the relative angle between the built-in hinge angle and the flow direction. Therefore, a critical concern is the behaviour of such a device at non-zero sideslip angles, such as experienced by aircraft in crosswind landings. In this paper, a specially designed wind tunnel model capable of large wingtip rotations, and a geometrically nonlinear numerical model, are utilised to explore how sideslip angle affects both the static and dynamic behaviour of such a system. It is shown that stable equilibrium positions exist up to and beyond a fold angle of 90 degrees, even when the effective flare angle is zero or switches sign. Additionally, to accurately capture the variation in the frequency of the wingtip with sideslip angle, it is shown factors such as the change in sweep angle of the wing must be accounted for. Furthermore, it is shown that these changes in frequency with sideslip angle can lead to a reduction in the flutter speed, but do not have a significant impact on the gust load alleviation of wings incorporating FFWTs, when exposed to one-minus-cosine gust encounters

Identification of backbone curves of nonlinear systems from resonance decay responses

AbstractBackbone curves can offer valuable insight into the behaviour of nonlinear systems along with significant information about any coupling between the underlying linear modes in their response. This paper presents a technique for the extraction of backbone curves of lightly damped nonlinear systems that is well suited for the experimental investigation of structures exhibiting nonlinear behaviour. The approach is based on estimations of the instantaneous frequency and the envelope amplitude of a decaying response following a tuned steady-state oscillation of the system. Results obtained from simulations and experiments demonstrate that the proposed procedure is capable of achieving an accurate estimation of the backbone curves and damping ratios of the system provided that the premise of damping having low impact on its oscillation frequency is met