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Stability Analysis of a Multi-Degree of Freedom System Limit Cycles and Close Trajectories

[+] Author Affiliations
Jiŕí Náprstek

Institute of Theoretical and Applied Mechanics, v.v.i., Prague, Czech Republic

Paper No. IMECE2010-38147, pp. 981-990; 10 pages
  • ASME 2010 International Mechanical Engineering Congress and Exposition
  • Volume 8: Dynamic Systems and Control, Parts A and B
  • Vancouver, British Columbia, Canada, November 12–18, 2010
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4445-8
  • Copyright © 2010 by ASME


Limit cycles (LC) are important steady state response types of multi-degree of freedom (MDOF) systems. Problems of LC basic existence, their emerging and extinction are closely related with their stable/unstable character. A new analytical/iterative method of LC identification and portrait investigation has been developed together with a technique of stability assessment. It enables to distinguish the stable/unstable limit cycles and consequently to define the attractive and repulsive response fields. LC investigation and transition processes from/to the wide attractor are carried out in subspace which is normal to the limit cycle trajectory. Special orthogonal subsystem is constructed. It enables an effective investigation of an LC behavior in a close neighborhood of the basic trajectory. Some analogies and relations with Lyapunov exponent procedure are mentioned. The general theoretical background is demonstrated on an SDOF and later DDOF systems. Links with related areas of non-linear dynamics and some open problems are outlined.

Copyright © 2010 by ASME
Topics: Stability , Cycles



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