Global and bifurcation analysis of a structure with cyclic symmetry

This article combines the application of a global analysis approach and the more classical continuation, bifurcation and stability analysis approach of a cyclic symmetric system. A solid disc with four blades, linearly coupled, but with an intrinsic non-linear cubic stiffness is at stake. Dynamic eq...

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Bibliographic Details
Published in:International journal of non-linear mechanics 2011-06, Vol.46 (5), p.727-737
Main Authors: Sarrouy, E., Grolet, A., Thouverez, F.
Format: Article
Language:English
Subjects:
Bifurcations
Cyclic symmetry
Discs
Dynamical systems
Engineering Sciences
Global analysis
Homotopy
Mathematical analysis
Mechanics
Non-linear
Nonlinear dynamics
Nonlinearity
Physics
Pulsation
Rotordynamics
Stability analysis
Structural mechanics
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Summary:This article combines the application of a global analysis approach and the more classical continuation, bifurcation and stability analysis approach of a cyclic symmetric system. A solid disc with four blades, linearly coupled, but with an intrinsic non-linear cubic stiffness is at stake. Dynamic equations are turned into a set of non-linear algebraic equations using the harmonic balance method. Then periodic solutions are sought using a recursive application of a global analysis method for various pulsation values. This exhibits disconnected branches in both the free undamped case (non-linear normal modes, NNMs) and in a forced case which shows the link between NNMs and forced response. For each case, a full bifurcation diagram is provided and commented using tools devoted to continuation, bifurcation and stability analysis.
ISSN:0020-7462
1878-5638
DOI:10.1016/j.ijnonlinmec.2011.02.005