TY - JOUR
T1 - Parametric stabilization of a gyroscopic system
AU - McDonald, R. J.
AU - Sri Namachchivaya, N.
N1 - Funding Information:
The authors would like to acknowledge the support of the O$ce of Naval Research under grant number N000140110647, and National Science Foundation under grant number CMS 00-84944.
PY - 2003/8/22
Y1 - 2003/8/22
N2 - 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.
AB - 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.
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U2 - 10.1006/jsvi.2001.4182
DO - 10.1006/jsvi.2001.4182
M3 - Article
AN - SCOPUS:0037461479
SN - 0022-460X
VL - 255
SP - 635
EP - 662
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
IS - 4
ER -