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On the numerical approximation of invariant manifolds for quasiperiodic motions
Author(s) -
Fiedler Robert,
Hetzler Hartmut
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710155
Subject(s) - quasiperiodic function , invariant (physics) , invariant manifold , manifold (fluid mechanics) , statistical physics , rotor (electric) , mathematics , dynamical systems theory , classical mechanics , control theory (sociology) , physics , mathematical analysis , computer science , engineering , mathematical physics , control (management) , mechanical engineering , quantum mechanics , artificial intelligence
The interference of oscillations with different physical origins with incommensurable frequencies can lead to quasiperiodic motions. Concerning engineering problems, there is a variety of models which exhibit multi frequent oscillations. This contribution proposes a numerical approach approximating stationary solutions by an invariant manifold. To apply the approach a partitioning of the phase variables is necessary, which defines the parametrisation of a dynamical system. In order to demonstrate the applicability of the proposed method, stationary solutions of an unbalanced Laval‐rotor (Jeffcott‐rotor) are calculated and continued under variation of a control parameter. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)