Browsing by Author "Lindholm, Brian Eric"

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    A Bayesian statistics approach to updating finite element models with frequency response data
    Lindholm, Brian Eric (Virginia Tech, 1996-08-05)
    This dissertation addresses the task of updating finite element models with frequency response data acquired in a structural dynamics test. Standard statistical techniques are used to generate statistically qualified data, which is then used in a Bayesian statistics regression formulation to update the finite element model. The Bayesian formulation allows the analyst to incorporate engineering judgment (in the form of prior knowledge) into the analysis and helps ensure that reasonable and realistic answers are obtained. The formulation includes true statistical weights derived from experimental data as well as a new formulation of the Bayesian regression problem that reduces the effects of numerical ill-conditioning. Model updates are performed with a simulated free-free beam, a simple steel frame, and a cantilever beam. Improved finite element models of the structures are obtained and several statistical tests are used to ensure that the models are improved.
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    Reconciliation of a Rayleigh-Ritz beam model with experimental data
    Lindholm, Brian Eric (Virginia Tech, 1994-09-05)
    In order to perform structural optimization and/or modification on a structure, an analytical model which sufficiently describes the behavior of the structure must be developed. Analytical models can be generated for almost any structure, but such a model will generally not effectively predict the behavior of the structure unless the model is somehow reconciled with experimental data taken from the structure. Additionally, the model must also be complete, i.e., it must not only model the structure but also model any suspension system used to support the structure. If the suspension is not included in the model, any attempt to reconcile the model with experimental data will result in a incorrect model. Using this incorrect model to perform structural modification cannot be expected to give correct results. In this thesis, an approach for estimating the effects of a suspension system on the flexural vibration of a structure is developed. These effects are treated mathematically as variations in boundary conditions. Topics discussed include formulation of an analytical model that includes suspension effects, experimental methods for acquiring mode shapes which exhibit these effects, and reconciliation techniques for matching analytical mode shapes to experimental mode shapes to determine the effective boundary conditions.