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Nonholonomically Constrained Dynamics and Optimization of Rolling Isolation Systems

dc.contributor.advisor Gavin, Henri P Kelly, Karah 2016-06-06T16:50:23Z 2018-05-10T08:17:10Z 2016
dc.description.abstract <p>Rolling Isolation Systems provide a simple and effective means for protecting components from horizontal floor vibrations. In these systems a platform rolls on four steel balls which, in turn, rest within shallow bowls. The trajectories of the balls is uniquely determined by the horizontal and rotational velocity components of the rolling platform, and thus provides nonholonomic constraints. In general, the bowls are not parabolic, so the potential energy function of this system is not quadratic. This thesis presents the application of Gauss's Principle of Least Constraint to the modeling of rolling isolation platforms. The equations of motion are described in terms of a redundant set of constrained coordinates. Coordinate accelerations are uniquely determined at any point in time via Gauss's Principle by solving a linearly constrained quadratic minimization. In the absence of any modeled damping, the equations of motion conserve energy. This mathematical model is then used to find the bowl profile that minimizes response acceleration subject to displacement constraint.</p>
dc.subject Civil engineering
dc.subject Constrained Dynamical Systems
dc.subject Non-Linear Dynamics
dc.subject Optimization
dc.subject Rolling Isolation System
dc.subject Vibration Isolation
dc.title Nonholonomically Constrained Dynamics and Optimization of Rolling Isolation Systems
dc.type Master's thesis
dc.department Civil and Environmental Engineering
duke.embargo.months 23

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