Bloch analysis was originally developed by Felix Bloch to solve Schrödinger's equation for the electron wave function in a periodic potential field, such as that found in a pristine crystalline solid. His method has since been adapted to study elastic wave propagation in periodic structures. The absence of a rigorous mathematical analysis of the approach, as applied to periodic structures, has resulted in mistreatment of internal forces and misapplication to nonlinear media. In this thesis, we detail a mathematical basis for Bloch analysis and thereby shed important light on the proper application of the technique. We show conclusively that translational invariance is not a proper justification for invoking the existence of a "propagation constant," and that in nonlinear media this results in a flawed analysis. Next, we propose a general framework for applying Bloch analysis in damped systems and investigate the effect of damping on dispersion curves. In the context of Schrödinger's equation, damping is absent and energy is conserved. In the damped setting, application of Bloch analysis is not straight-forward and requires additional considerations in order to obtain valid results. Results are presented in which the approach is applied to example structures. These results reveal that damping may introduce wavenumber band gaps and bending of dispersion curves such that two or more temporal frequencies exist for each dispersion curve and wavenumber. We close the thesis by deriving conditions which predict the number of wavevectors at each frequency in a dispersion relation. This has important implications for the number of nearest neighbor interactions that must be included in a model in order to obtain dispersion predictions which match experiment.

No description available.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Wheel loaders are under the influence of low frequency vibrations that may be harmful for the health of the operator, and for the productivity of the machine. The strong vibrations can significantly impact the operation of the machine since they are not equipped with wheel suspension systems and due to their work environment in rough terrains with uneven surfaces. The risk of spilling or dropping the load is also increased and they can introduce higher mechanical stress that can wear out parts faster. The focus of this thesis work is to develop an approach for damping these vibrations dynamically by improving the functionality of the electrohydraulic system in Volvo's prototype wheel loader LX1. The dynamic damping system controls the cylinder of the lift framework to make it behave as a damper. The system utilizes the lift cylinder pressure and piston position as feedback to adjust the oil flow in the cylinder using the proposed control system. Results indicate that the proposed technique is capable of attenuation that is comparable with the existing boom suspension system based on accumulators through simulations and experimental tests.

Vibrating machinery like rock drills and compactors are becoming more prominent in modem industry. The vibrations of these machines can damage surrounding structures and foundations and be harmful to their operators. Hand arm vibration syndrome is one example of serious injuries suffered by operators of these machines. Due to the fact that these machines need to vibrate, vibration absorbers that minimise the vibrations of the machines cannot be used. In such cases vibration isolators are necessary to isolate the vibration between the vibrating machine and other bodies like the handle or foundations. A tuned vibration isolator is a type of isolator that is able to isolate a certain frequency very effectively. These isolators can retain low mass and high stiffness compared to traditional isolators and can obtain complete isolation at the isolation frequency if no damping is present. The liquid inertia vibration eliminator (LIVE) is such a tuned vibration isolator that makes use of hydraulic amplification, which result in a very compact design. A LIVE isolator was designed incorporating the variable stiffness spring and a variable damping mechanism. Equations for the damped natural and isolation frequency of the LIVE isolator were also derived. The reason for changing the stiffness was to be able to adjust the isolation frequency of the isolator to coincide with the excitation frequency that resulted in a more effective isolator. The variable stiffness spring consisted of two leaf springs mounted on top of each other and separated at the centre to stiffen the whole spring assembly. The leaf springs were separated by a wax actuator that was controlled with a closed loop displacement control system to form a smart actuator. A stiffness change of 2.7 times the original stiffness was obtained by separating the springs. The variable damping mechanism was to be able to control the amount of amplification of noise at the natural frequency. An experimental isolator was built and tested and resulted in a tunable vibration isolator. The isolation frequency of the isolator could be shifted from 22.8 Hz to 36.2 Hz and a transmissibility of 10% was achieved over that whole range. The variable damping mechanism increased the viscous damping ratio from 0.001 to 0.033. A control system was designed and implemented that tuned the isolator automatically to the excitation conditions. It incorporated an optimisation algorithm to determine the optimum settings and then kept the isolator at that setting until the excitation conditions change. The whole process was then repeated. A tunable vibration isolator was therefore successfully developed that can be used to isolate tonal vibrations very effectively. The isolation frequency and damping of the isolator can be changed while in operation and a transmissibility of 10% can be achieved at the isolation frequency. / Thesis (M Eng (Mechanical Engineering))--University of Pretoria, 2006. / Mechanical and Aeronautical Engineering / unrestricted

The aim of the submitted diploma thesis is the magnitude determination of the headlamp response to the dynamic excitation. Currently it is necessary to measure this response, because it is one of the assessed criteria of quality of the headlamp. When comparing results of the experimental measurement and the computational modelling, a good consensus of resonant frequencies is observed, but there are significant differences in acceleration amplitudes. The cause of this is the variable damping value. The theoretical part of the thesis deals with polymeric materials, basics of oscillation and damping. It serves to understand the mechanisms, which influence the results of the experimental measurement. The practical part is dedicated to the procedure of the computational modelling and the experimental measurement implementation. The analysis of the experimental measurement results leads to an ascertainment of nonlinearities, which influence the headlamp behaviour. The results of a sensitivity analysis of the computational modelling are used to create curves, on the basis of which the damping is estimated. The inclusion of the estimated damping into computational modelling leads to reduction of the compared differences of the acceleration amplitudes. The conclusion of the thesis contains the recommendation for the damping determination during the computational modelling of the headlamp.

No description available.

No description available.

The optical power of satellites such as the Hubble telescope is directly related to the size of the primary mirror. However, due to the limited capacity of the shuttle bay, progress towards the development of more powerful satellites using traditional construction methods has come to a standstill. Therefore, to allow larger satellites to be launched into space significant interest has been shown in the development of ultra large inflatable structures that can be packaged inside the shuttle bay and then deployed once in space. To facilitate the packaging of the inflated device in its launch configuration, most structures utilize a thin film membrane as the optical or antenna surface. Once the inflated structure is deployed in space, it is subject to vibrations induced mechanically by guidance systems and space debris as well as thermally induced vibrations from variable amounts of direct sunlight. For the optimal performance of the satellite, it is crucial that the vibration of the membrane be quickly suppressed. However, due to the extremely flexible nature of the membrane structure, few actuation methods exist that avoid local deformation and surface aberrations. One potential method of applying damping to the membrane structure is to use magnetic damping. Magnetic dampers function through the eddy currents that are generated in a conductive material that experiences a time varying magnetic field. However, following the generation of these currents, the internal resistance of the conductor causes them to dissipate into heat. Because a portion of the moving conductor's kinetic energy is used to generate the eddy currents, which are then dissipated, a damping effect occurs. This damping force can be described as a viscous force due to the dependence on the velocity of the conductor. While eddy currents form an effective method of applying damping, they have normally been used for magnetic braking applications. Furthermore, the dampers that have been designed for vibration suppression have typically been ineffective at suppressing structural vibration, incompatible with practical systems, and cumbersome to the structure resulting in significant mass loading and changes to the dynamic response. To alleviate these issues, three previously unrealized damping mechanisms that function through eddy currents have been developed, modeled and tested. The dampers do not contact the structure, thus, allowing them to add damping to the system without inducing the mass loading and added stiffness that are typically common with other forms of damping. The first damping concept is completely passive and functions solely due to the conductor's motion in a static magnetic field. The second damping system is semi-active and improves the passive damper by allowing the magnet's position to be actively controlled, thus, maximizing the magnet's velocity relative to the beam and enhancing the damping force. The final system is completely active using an electromagnet, through which the current can be actively modified to induce a time changing magnetic flux on the structure and a damping effect. The three innovative damping mechanisms that have resulted from this research apply control forces to the structure without contacting it, which cannot be done by any other passive vibration control system. Furthermore, the non-contact nature of these dampers makes them compatible with the flexible membranes needed to advance the performance of optical satellites. / Ph. D.

Aircraft and satellite structures are exposed to a wide range of temperatures during normal operation cycles. These fluctuations in temperature may result in significant changes of the structural dynamics. Aircraft, automotive, and satellite structures are also subject to various vibration sources. Passive and active vibration suppression techniques have been developed to minimize acoustic noise and fatigue stress damage. Featuring low weight solutions and high performance, active control techniques are becoming increasingly common. Structures with varying dynamics require more sophisticated active control techniques, such as adaptive control. This research uses a special vibration test rig for evaluating the performance of different vibration suppression systems on a representative aircraft panel. The test panel is clamped rigidly in a frame and can be excited in various frequencies with an electromagnetic shaker. To simulate temperature fluctuations the temperature on the panel can be increased up to 65°C (150°F). Smart material based sensors and actuators are used to interface the mechanical system with the electronic controller. The active controller utilizes three positive position feedback (PPF) filters implemented through a digital signal processor board. This research develops two different adaptation methods to perform vibration suppression in the presence of thermally induced frequency changes of the representative panel. To adjust the PPF filter parameters an open-loop adaptation method and an auto-tuning method are investigated. The open-loop adaptation method uses a measurement of the plate temperature and a look-up table with pre-determined parameters to update the filters accordingly. The auto-tuning methods identifies the frequencies of the poles and zeros in the structure's collocated transfer function. From the knowledge of the pole and zero locations the optimal PPF parameters are calculated online. The results show that both adaptation methods are capable of reducing the vibration levels of the test specimen over the temperature range of interest. Three PPF filters with parameter adaptation through temperature measurement achieve magnitude reductions of the resonance peaks as high as 13.6 decibel. Using the auto-tuning method resonance peak reductions up to 17.4 decibel are possible. The pole/zero identification routine proves to detect the frequencies correctly. The average identification error remained at around one percent even in the presence of external disturbances. / Master of Science