Journal of System Design and Dynamics
Online ISSN : 1881-3046
ISSN-L : 1881-3046
Invited Reviews (Special Issue)
Parametric Resonance in Mechanics: Classical Problems and New Results
Alexander P. SEYRANIAN
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2008 Volume 2 Issue 3 Pages 664-683

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Abstract
We formulate and solve parametric resonance problems for one- and multiple degrees of freedom systems in three-dimensional space of physical parameters: excitation frequency, amplitude, and viscous damping coefficient assuming that the last two parameters are small. The main result obtained here is that we find the instability domains (simple and combination parametric resonances) as half-cones in three-parameter space with the use of eigenfrequencies and eigenmodes of the corresponding conservative system.
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© 2008 by The Japan Society of Mechanical Engineers
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