3-dimensional flutter kinematic structural stability

Having recalled the kinematic structural stability (ki.s.s) issue and its solution for divergence-type instability, we address the same problem for flutter-type instability for the minimal required configuration of dimensions—meaning 3 degree of freedom systems. We first get a sufficient non optimal...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2016-06, Vol.29, p.19-37
Main Authors: Lerbet, J., Hello, G., Challamel, N., Nicot, F., Darve, F.
Format: Article
Language:English
Subjects:
Degrees of freedom
Differential geometry
Engineering Sciences
Flutter stability domain
Grassmann manifolds
Instability
Kinematics
Mathematical analysis
Mechanics
Optimization
Stability
Structural stability
Vibration
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Summary:Having recalled the kinematic structural stability (ki.s.s) issue and its solution for divergence-type instability, we address the same problem for flutter-type instability for the minimal required configuration of dimensions—meaning 3 degree of freedom systems. We first get a sufficient non optimal condition. In a second time, the complete issue is tackled by two different ways leading to same results. A first way using calculations on Grassmann and Stiefel manifolds that may be generalized for any dimensional configuration. A second way using the specific dimensional configuration is brought back to calculations on the sphere. Differences with divergence ki.s.s are highlighted and examples illustrate the results.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2015.10.006