On the numerical approximation of invariant manifolds for quasiperiodic motions | Zendy

Fiedler Robert | Zendy; Hetzler Hartmut | Zendy

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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)

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