Non-linear evolution of a second mode wave in supersonic boundary layers

The nonlinear time evolution of a second mode instability in a Mach 4.5 wall-bounded flow is computed by solving the full compressible, time-dependent Navier-Stokes equations. High accuracy is achieved by using a Fourier-Chebyshev collocation algorithm. Primarily inviscid in nature, second modes are characterized by high frequency and high growth rates compared to first modes. Time evolution of growth rate as a function of distance from the plate suggests this problem is amenable to the Stuart-Watson perturbation theory as generalized by Herbert

Theoretical Results Supporting the Use of Passive Damping as Augmentation to the Active Control of Flexible Structures

One challenge of modern control technology is how to control a flexible structure with accuracy, speed, and economy of effort. Controlling a structure with many degrees of freedom by purely active means implies the implementation of inordinate sensors and actuators and creates the need for numerous calculations that must be done instantly. Experiments have shown that practical structures under active control alone can suffer instabilities due to modal vibrations beyond the bandwidth of the active controller. Furthermore, if there is a high degree of model uncertainty, instabilities can be produced by inputs of modal vibrations not occurring in the system model. The use of passive damping to stabilize those vibrations beyond the domain of the active controller and to help reduce the effects of model uncertainty has been shown to be critical to enabling control of flexible structures. The question remains as to how passive damping should best be implemented to aid active control. The same amount of damping (by weight) can be applied in different ways--some ways may satisfy performance constraints, while others may not. Part I of this thesis deals with the effects of damping on control. The system to be controlled is defined by its linear matrix differential equation. The system is under the influence of a disturbance and a set of control forces. A performance index is defined, after which are derived closed-form expressions for the optimal feedback gains and the optimal value of the performance index. A modern passive damping technique is applied to a beam, and the cost function is optimized subject to the appropriate constraints. The benefits of the damping are demonstrated in the performance, the displacement output, and in the economic savings. Part II of this thesis pursues the effects of passive damping on plant model reduction in modal coordinates. Prevailing closed-form expressions in this field assume light damping and widespread natural frequencies. A formula is derived based upon general constant-ratio damping and general spectrum of natural frequencies. Conclusions are drawn, and numerical examples demonstrate the effects of this new formula on model reduction as the modal damping ratio is varied

Anatomy and efficiency of urban multimodal mobility

International audienceThe growth of transportation networks and their increasing interconnections, although positive,has the downside effect of an increasing complexity which make them difficult to use, to assess, andlimits their efficiency. On average in the UK, 23% of travel time is lost in connections for trips withmore than one mode, and the lack of synchronization decreases very slowly with population size.This lack of synchronization between modes induces differences between the theoretical quickest tripand the ‘time-respecting’ path, which takes into account waiting times at interconnection nodes.We analyse here the statistics of these paths on the multilayer, temporal network of the entire,multimodal british public transportation system. We propose a statistical decomposition – the‘anatomy’ – of trips in urban areas, in terms of riding, waiting and walking times, and which showshow the temporal structure of trips varies with distance and allows us to compare different cities.Weaknesses in systems can be either insufficient transportation speed or service frequency, but thekey parameter controlling their global efficiency is the total number of stop events per hour for allmodes. This analysis suggests the need for better optimization strategies, adapted to short, longunimodal or multimodal trips