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dc.contributor.authorNave Jr, Gary Kirken_US
dc.date.accessioned2018-09-01T08:00:53Z
dc.date.available2018-09-01T08:00:53Z
dc.date.issued2018-08-31
dc.identifier.othervt_gsexam:16851en_US
dc.identifier.urihttp://hdl.handle.net/10919/84945
dc.description.abstractThis dissertation presents useful nonlinear models for fluid forcing on a moving body in two distinct contexts, and methods for analyzing the geometric structure within those and other mathematical models. This manuscript style dissertation presents three works within the theme of understanding fluid forcing and geometric structure. When a bluff body is free to move in the presence of an incoming bluff body wake, the average forcing on the body is dependent on its position relative to the upstream bluff body. This position-dependent forcing can be conceptualized as a stiffness, much like a spring. This work presents an updated model for the quasi-steady fluid forcing of a wake and extends the notion of wake stiffness to consider a nonlinear spring. These results are compared with kinematic experimental results to provide an example of the application of this framework. Fluid force models also play a role in understanding the behavior of passive aerodynamic gliders, such as gliding animals or plant material. The forces a glider experiences depend on the angle that its body makes with respect to its direction of motion. Modeling the glider as capable of pitch control, this work considers a glider with a fixed angle with respect to the ground. Within this model, all trajectories in velocity space collapse to a 1-dimensional invariant manifold known as the terminal velocity manifold. This work presents methods to identify the terminal velocity manifold, investigates its properties, and extends it to a 2-dimensional invariant manifold in a 3-dimensional space. Finally, in the search for manifolds such as the terminal velocity manifold, this dissertation introduces a new diagnostic for identifying the low dimensional geometric structure of models. The trajectory divergence rate uses instantaneous vector field information to identify regions of large normal stretching and strong normal convergence between nearby invariant manifolds. This work lays out the mathematical basis of the trajectory divergence rate and shows its application to approximate a variety of structures including slow manifolds and Lagrangian coherent structures. This dissertation applies nonlinear theoretical and numerical techniques to analyze models of fluid forcing and their geometric structure. The tools developed in this dissertation lay the groundwork for future research in the fields of flow-induced vibration, plant and animal biomechanics, and dynamical systems.en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis item is protected by copyright and/or related rights. Some uses of this item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectFluid-structure interaction; phase space structure; computational geometry; nonlinear dynamicsen_US
dc.titleNonlinear Models and Geometric Structure of Fluid Forcing on Moving Bodiesen_US
dc.typeDissertationen_US
dc.contributor.departmentEngineering Science and Mechanicsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineEngineering Mechanicsen_US
dc.contributor.committeechairRoss, Shane Daviden_US
dc.contributor.committeechairStremler, Mark A.en_US
dc.contributor.committeememberAbaid, Nicole Teresaen_US
dc.contributor.committeememberSocha, Johnen_US
dc.contributor.committeememberWoolsey, Craig A.en_US


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