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Abstract:
The methodology for reduced order models of nonlinear dynamical systems is always of great interest in dynamics community. Recently, spectral submanifolds (SSMs) related to hyperbolic fixed points have been constructed and successfully used to build reduced order models for nonlinear systems with a large number of degrees of freedom. There are, however, few works on the spectral submanifolds associated with periodic orbits in literature. In this paper, SSM associated to the periodic orbit of a nonlinear normal mode (NNM) of a rotor/stator rubbing system with cross-coupling stiffness is first constructed following the parameterization method. The SSM with a two-dimensional slow sub-stable invariant manifold attached to the stable NNM with forward whirl also serves as a reduced order model of the system, whose dynamics on the parameter space conjugates the dynamics of the full system. Unlike the previous works, where reduced order models are mainly used to obtain backbones of conservative autonomous systems or FRCs of light damped forcing systems as the non-autonomous perturbation, the reduced order model derived from autonomous system are used to predict the self-excited dominant forcing responses of the rotor/stator rubbing system. As can be seen, the reduced order model is valid with good accuracy in some range of forcing amplitudes. Moreover, the modification of the reduced order model by considering forcing perturbation is also built and works well even in a larger range of forcing amplitudes. © 2022
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Source :
International Journal of Mechanical Sciences
ISSN: 0020-7403
Year: 2022
Volume: 228
5 . 3 2 9
JCR@2020
ESI Discipline: ENGINEERING;
ESI HC Threshold:7
Cited Count:
SCOPUS Cited Count: 7
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 6
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