Skip to main content
Duke University Libraries
DukeSpace Scholarship by Duke Authors
  • Login
  • Ask
  • Menu
  • Login
  • Ask a Librarian
  • Search & Find
  • Using the Library
  • Research Support
  • Course Support
  • Libraries
  • About
View Item 
  •   DukeSpace
  • Theses and Dissertations
  • Masters Theses
  • View Item
  •   DukeSpace
  • Theses and Dissertations
  • Masters Theses
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Nonholonomically Constrained Dynamics and Optimization of Rolling Isolation Systems

Thumbnail
View / Download
23.1 Mb
Date
2016
Author
Kelly, Karah
Advisor
Gavin, Henri P
Repository Usage Stats
233
views
60
downloads
Abstract

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.

Type
Master's thesis
Department
Civil and Environmental Engineering
Subject
Civil engineering
Constrained Dynamical Systems
Non-Linear Dynamics
Optimization
Rolling Isolation System
Vibration Isolation
Permalink
https://hdl.handle.net/10161/12324
Citation
Kelly, Karah (2016). Nonholonomically Constrained Dynamics and Optimization of Rolling Isolation Systems. Master's thesis, Duke University. Retrieved from https://hdl.handle.net/10161/12324.
Collections
  • Masters Theses
More Info
Show full item record
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.

Rights for Collection: Masters Theses


Works are deposited here by their authors, and represent their research and opinions, not that of Duke University. Some materials and descriptions may include offensive content. More info

Make Your Work Available Here

How to Deposit

Browse

All of DukeSpaceCommunities & CollectionsAuthorsTitlesTypesBy Issue DateDepartmentsAffiliations of Duke Author(s)SubjectsBy Submit DateThis CollectionAuthorsTitlesTypesBy Issue DateDepartmentsAffiliations of Duke Author(s)SubjectsBy Submit Date

My Account

LoginRegister

Statistics

View Usage Statistics
Duke University Libraries

Contact Us

411 Chapel Drive
Durham, NC 27708
(919) 660-5870
Perkins Library Service Desk

Digital Repositories at Duke

  • Report a problem with the repositories
  • About digital repositories at Duke
  • Accessibility Policy
  • Deaccession and DMCA Takedown Policy

TwitterFacebookYouTubeFlickrInstagramBlogs

Sign Up for Our Newsletter
  • Re-use & Attribution / Privacy
  • Harmful Language Statement
  • Support the Libraries
Duke University