The Finite Element Method (FEM) based computational mechanics is applied to simulate the optimal attenuation of vibrations in actively controlled structures. The simulation results provide the forces to be generated by actuators, as well as the structures response. Vibrations can be attenuated by applying either open loop or closed loop control strategies. In open loop control, the control forces for a given initial (or disturbed) configuration of the structure are determined in terms of time, and can be preprogrammed in advance. On the other hand, the control forces in closed loop control depend only on the current state of the system, which should be continuously monitored. Optimal attenuation is obtained by solving the optimality equations for the problem derived from the Pontryagins principle. These equations together with the initial and final boundary conditions constitute the two-point-boundary-value (TPBV) problem. <p>Here the optimal solutions are obtained by applying an analogy (referred to as the beam analogy) between the optimality equation and the equation for a certain problem of static beams in bending. The problem of analogous beams is solved by the standard FEM in the spatial domain, and then the results are converted into the solution of the optimal vibration control problem in the time domain. The concept of the independent-modal-space-control (IMSC) is adopted, in which the number of independent actuators control the same number of vibrations modes. <p>The steps of the analogy are programmed into an algorithm referred to as the Beam Analogy Algorithm (BAA). As an illustration of the approach, the BAA is used to simulate the open loop vibration control of a structure with several sets of actuators. Some details, such as an efficient meshing of the analogous beams and effective solving of the target condition are discussed. <p> Next, the BAA is modified to handle closed loop vibration control problems. The algorithm determines the optimal feedback gain matrix, which is then used to calculate the actuator forces required at any current state of the system. The methods accuracy is also analyzed.
| Identifer | oai:union.ndltd.org:USASK/oai:usask.ca:etd-04302004-080403 |
| Date | 30 April 2004 |
| Creators | Baweja, Manish |
| Contributors | Watson, L. Glen, Szyszkowski, Walerian, Oguocha, Ikechukwuka N., Burton, Richard T., Boulfiza, Mohamed |
| Publisher | University of Saskatchewan |
| Source Sets | University of Saskatchewan Library |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://library.usask.ca/theses/available/etd-04302004-080403/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Saskatchewan or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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