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Classification of Periodic Solutions in a Single-Degree-of-Freedom System With Backlash

[+] Author Affiliations
Bart Besselink, Rob Fey, Henk Nijmeijer

Eindhoven University of Technology, Eindhoven, The Netherlands

Amit Shukla

Miami University, Oxford, OH

Paper No. DETC2007-34236, pp. 173-182; 10 pages
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME


In this paper a single degree-of-freedom system with backlash is studied for its periodic response. This system is modeled as a piecewise linear system with discontinuity in the net restoring force, caused by additional damping in the contact-zone. The periodic orbits are classified by their number of subspace boundary crossings and Floquet multipliers. For this classification, the known analytical solutions in the different subspaces are used in the multiple shooting algorithm and a continuation method. Some observations are also presented about the qualitative features (such as symmetry, rigid body solutions) exhibited by this class of systems.

Copyright © 2007 by ASME



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