Vortices in (2+1)d Conformal Fluids

We study isolated, stationary, axially symmetric vortex solutions in (2+1)-dimensional viscous conformal fluids. The equations describing them can be brought to the form of three coupled first order ODEs for the radial and rotational velocities and the temperature. They have a rich space of solutions characterized by the radial energy and angular momentum fluxes. We do a detailed study of the phases in the one-parameter family of solutions with no energy flux. This parameter is the product of the asymptotic vorticity and temperature. When it is large, the radial fluid velocity reaches the speed of light at a finite inner radius. When it is below a critical value, the velocity is everywhere bounded, but at the origin there is a discontinuity. We comment on turbulence, potential gravity duals, non-viscous limits and non-relativistic limits.Comment: 39 pages, 10 eps figures, v2: Minor changes, refs, preprint numbe

Magnetic suspension and vibration control of flexible structures for non-contact processing

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2000.Includes bibliographical references (p. 365-372).This thesis presents the design, analysis, and experimental testing of systems for noncontact suspension and control of flexible structures. Our particular focus is on the use of such suspensions in manufacturing processes which can be facilitated by the ability to control workpiece motion without contact. This can be of significant utility in processes such as coating, painting, heat treating, and web handling. We develop a novel approach for the control of such non-contact suspensions through what we term sensor averaging and actuator averaging. The difficult stability and robustness problems imposed by the flexible dynamics of the workpiece can be overcome by taking a properly-weighted average of the outputs of a distributed array of N motion sensors (sensor averaging), and/or by applying a properly-weighted distributed array of M forces (actuator averaging) to the workpiece. The theory for these dual techniques is developed in detail in the thesis. These approaches are shown to be independent of the specific boundary conditions or the longitudinal dimensions of the workpiece. These approaches are thus generally applicable to a wide range of structural control problems. We present both analytical and numerical analyses of the structural dynamics for typical flexible workpieces such as strings, beams, membranes, and plates. The analyses include axial translation of the workpiece. We have experimentally demonstrated the utility of our theory by application in the successful magnetic suspension of a 3 m long, 6.35 mm diameter, 0.89 mm wall thickness steel tube with varying boundary conditions. This is a very challenging problem due to the extremely light damping of the modes (< 0.001 with free ends). The experiment uses a set of 8 sensors and 8 actuators to measure and control the motion of the tube in the two lateral degrees of freedom. We present the details of the developed electromagnetic actuators, position sensors, modeling of the structural dynamics, the relevant vibration control techniques, and develop the associated theory for choosing sensor and actuator locations. Our results experimentally confirm the value of our averaging techniques, and suggest the wide future application of these ideas in industrial processes which require non-contact handling of workpieces.by Ming-chih Weng.Ph.D

Boundary control of flexible mechanical systems

Ph.DDOCTOR OF PHILOSOPH

Modeling and Control of Marine Flexible Systems

Ph.DDOCTOR OF PHILOSOPH

Nonlinear Dynamics

This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students

Machine generated vertical vibration in elevators

Vertical vibration deteriorates passenger comfort during an elevator travel. The drive system is a source of vertical vibration as well as the source of energy of the system. This report presents the results of a study of car vertical vibrations generated at the drive system in elevator installations. The elevator system can be considered as a translating assembly of inertia elements coupled and constrained by one-dimensional slender continua. The inertia elements are the car assembly, the counterweight, the traction sheave and other rotating components of the system. According to the roping arrangement and to the ratio of the tangential velocity of the traction sheave to the velocity of the car, the traction elevators can be classified as roped 1:1 or multiple reeving systems: the types examined in the present work are 1:1 and 2:1 traction elevators. Distributed- and lumped-parameter models (DPM and LPM respectively) are developed to calculate the natural frequencies and mode shapes of stationary elevator systems and their results compared. A non-stationary model of a 1:1 roping configuration elevator is developed as well to simulate the elevator acceleration response. The model accommodates the drive system dynamics: it includes the electric motor and the torque and velocity controllers, which ensure that the car follows a prescribed kinematic profile, so that good ride quality of the elevator is achieved. The machine parameters are computed by means of the Finite Element Method simulation software FLUX. With respect to the carcounterweight-sheave-ropes assembly, a LPM and a novel DPM are developed. The elevator dynamics represented by the DPM is described by a partial differential equation set that is discretised by expanding the vertical displacements in terms of the linear stationary mode shapes of a system composed of three masses constrained by the suspension rope. The models are implemented in the MATLAB/Simulink computational environment and the system response is determined through numerical simulation. It is shown that the LPM forms a good approximation of the DPM. Experimental tests are carried out on laboratory models. The elasticity modulus of the rope and the friction coefficients at the guide rail contact and at the machine are estimated. The acceleration response at the suspended masses and at the drive machine, the machine shaft velocity and the three phase current intensities supplied to the machine are measured during several travels. The machine torque is estimated from the current intensities. The computed and measured accelerations are compared either in time or frequency domain and it is demonstrated that the elevator car vibrates at frequencies generated at the machine, especially when they are close to the system natural frequencies. The proposed simulation models can be used as design and analysis tools in the development of high-performance elevator systems

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Development of a true triaxial apparatus for soil testing

This thesis presents the development of a True Triaxial Testing TTT Apparatus. The TTT apparatus developed has the capabilities of applying the three principal stresses to a rectangular prismoidal specimen independently. The minor principal stress is provided by the cell pressure. The major principal stress is provided by a load actuator traveling at a constant velocity. A LabView software program instantaneously reads instrumentation, makes calculations, and commands a second load actuator to induce an intermediate principal stress that maintains a constant b-value; where b-value is equal to the intermediate principal stress minus the minor principal stress divided by the major principal stress minus the minor principal stress. The development of the TTT Apparatus included; creating a robust data acquisition system to facilitate immediate readings of all needed instrumentation, manufacturing a horizontal loading system to transmit the load from the load actuator to the specimen, constructing a pressure control system capable of providing the desired confining pressure, creating a LabView software program to interface with the data acquisition system and the load actuators to record and control the test parameters. Calibration tests were performed to quantify the correction factors for the following: volume change due to volumetric expansion of the pressure jacket and loading rams, the load due to frictional forces and pressure, and the length change due to compression of the rubber cushions. True triaxial test were conducted on F-75 silica sand at various b-values as verification of the developed TTT Apparatus’s capabilities. The results of these tests compared well with the findings of other researchers conducting similar tests

The effect of well path, tortuosity and drillstring design on the transmission of axial and torsional vibrations from the bit and mitigation control strategies

As well designs become increasingly complicated, a complete understanding of drillstring vibrations is key to maximize drilling efficiency, to reduce drillstring dysfunction and to minimize drillstring, tool, and borehole damage. Torque and drag models exist that seek to quantify the effects of borehole inclination and tortuosity on static friction along the drillstring; however, the effects on dynamic friction remains poorly understood. This dissertation begins with a review of the past fifty years of work on drillstring dynamics models, an overview of the proposed control strategies and a summary deployed vibration mitigation applications within the drilling industry. Derivations from first principles of a series of computationally efficient axial and torsional drillstring models in both the frequency and time domains are then presented and verified with field data. The transfer matrix approach is used to predict the severity of axial vibrations along the drillstring and is verified using a series of case studies using field data. Harmonic axial vibrations within drillstrings are either induced intentionally, in the case of axial oscillation tools midway along the drillstring, or unintentional, in the case of bit bounce. Two case studies of bit bounce are first evaluated to ensure model validity for a harmonic excitation at a the bit and the model is found to accurately predict bit bounce based on surface rotation rates. Induced axial oscillations, generated by axial oscillation tools, are then investigated to quantify friction reduction and drilling efficiency improvements. Optimal placement is found to depend on wellbore geometry, but is usually restricted to periodic regions of the drillstring. These optimizations are then verified using field trials and suggest that improved placement can result in 20% or more reduction in friction along the drillstring. Two applications of torsional drillstring vibrations are then investigated -- stick slip mitigation and drillstring imaging. The time domain form of the torsional drillstring model is used first to evaluate the effectiveness of three types of top drive controllers -- stiff controllers, tuned PI controllers and impedance matching controllers -- in mitigating stick slip oscillations. Then, the transfer matrix method is applied to evaluate the effect of wellbore geometry on drillstring mobility to conclude that higher order modes of stick slip may become dominant in non-vertical wellbores. The feasibility of drillstring imaging using torsional signals from surface is then investigated to identify inputs and methods that show promise in three setups of varying complexity -- a hanging beam, a laboratory drillstring model and a drilling rig. Two techniques show promise -- white noise injection and model fitting of a step response -- in identifying larger features, including drillstring length and BHA location. However, low sampling frequencies and low bandwidth inputs reduce the ability to image small features such as friction points along the wellpath.Petroleum and Geosystems Engineerin