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Approximation of Periodic and Quasi‐Periodic Motions of a Rotor System with Visco‐elastic Seal Support by Using a Fourier‐Galerkin‐Method
Author(s) -
Bäuerle Simon,
Hetzler Hartmut
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800161
Subject(s) - fourier series , galerkin method , rotor (electric) , seal (emblem) , fourier transform , helicopter rotor , torus , periodic function , fourier analysis , mechanics , physics , classical mechanics , mathematical analysis , mathematics , geometry , finite element method , art , quantum mechanics , visual arts , thermodynamics
Abstract In this contribution a Fourier‐Galerkin method is used to calculate the periodic and quasi‐periodic motions of a rotor‐seal system. The system consists of a classical Laval ‐rotor, a visco‐elastically supported rigid seal rigid and a turbulent fluid flow through the seal gap. The Fourier‐Galerkin method uses one‐ and two‐dimensional Fourier series to approximate steady‐state periodic solutions due to rotor mass unbalance and quasi‐periodic solutions due to unbalance and self‐excitation stemming from the seal fluid forces. The method is applied to continue solution‐branches of the rotor‐seal system which show periodic/ quasi‐periodic solutions, resonance, multiple Neimark‐Sacker bifurcations as well as synchronisation (Torus‐breakdown).