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Characterization of the dynamic response of continuous system discretized using finite element methods

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dc.contributor.advisor Klaus-Jürgen Bathe. en_US Rugonyi, Sandra, 1970- en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mechanical Engineering. en_US 2012-09-13T18:51:58Z 2012-09-13T18:51:58Z 2001 en_US 2001 en_US
dc.description Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2001. en_US
dc.description Includes bibliographical references (leaves 122-125). en_US
dc.description.abstract Nonlinear dynamic physical systems exhibit a rich variety of behaviors. In many cases, the system response is unstable, and the behavior may become unpredictable. Since an unstable or unpredictable response is usually undesirable in engineering practice, the stability characterization of a system's behavior becomes essential. In this work, a numerical procedure to characterize the dynamic stability of continuous solid media, discretized using finite element methods, is proposed. The procedure is based on the calculation of the maximum Lyapunov characteristic exponent (LCE), which provides information about the asymptotic stability of the system response. The LCE is a measure of the average divergence or convergence of nearby trajectories in the system phase space, and a positive LCE indicates that the system asymptotic behavior is chaotic, or, in other words, asymptotically dynamically unstable. In addition, a local temporal stability indicator is proposed to reveal the presence of local dynamic instabilities in the response. Using the local stability indicator, dynamic instabilities can be captured shortly after they occur in a numerical calculation. The indicator can be obtained from the successive approximations of the response LCE calculated at each discretized time step. Both procedures can also be applied to fluid-structure interaction problems in which the analysis focuses on the behavior of the structural part. en_US
dc.description.abstract (cont.) The response of illustrative structural systems and fluid flow-structure interaction systems, in which the fluid is modeled using the Navier-Stokes equations, was calculated. The systems considered present both stable and unstable behaviors, and their LCEs and local stability indicators were computed using the proposed procedures. The stability of the complex behaviors exhibited by the problems considered was properly captured by both approaches, confirming the validity of the procedures proposed in this work. en_US
dc.description.statementofresponsibility by Sandra Rugonyi. en_US
dc.format.extent 125 leaves en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri en_US
dc.subject Mechanical Engineering. en_US
dc.title Characterization of the dynamic response of continuous system discretized using finite element methods en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mechanical Engineering. en_US
dc.identifier.oclc 48981161 en_US

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