Parametric stabilization of a gyroscopic system

R. J. McDonald, N. Sri Namachchivaya

Research output: Contribution to journalArticlepeer-review


This paper studies the stabilization of a gyroscopic system using parametric stabilization near a combination resonance. The gyroscopic system is near its primary instability, i.e., the bifurcation parameter is such that the system possesses a double zero eigenvalue. The stability of the system is studied for the linear Hamiltonian system, the damped linear system, the forced linear Hamiltonian system, and finally the damped and forced linear system. The addition of the periodic excitation near the critical combination resonance provides the system with an extended stability region when the excitation frequency is slightly above the combination resonance. A non-linear numerical example shows that these results may persist for the non-linear problem. The results of this work, are then discussed in relation to an example gyroscopic problem, a rotating shaft with periodically perturbed rotation rate.

Original languageEnglish (US)
Pages (from-to)635-662
Number of pages28
JournalJournal of Sound and Vibration
Issue number4
StatePublished - Aug 22 2003

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Acoustics and Ultrasonics


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