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On the motion of a generalized Van der Pol oscillator: influence of the fractional-order restoring and damping force

On the motion of a generalized Van der Pol oscillator: influence of the fractional-order restoring and damping force
On the motion of a generalized Van der Pol oscillator: influence of the fractional-order restoring and damping force
A generalized van der Pol oscillator is considered, with the positive real power nonlinearities in the restoring and damping force, including fractional powers. An analytical approach based on the Krylov–Bogoliubov method is utilized to derive approximate expressions for the amplitude of a limit cycle for small values of the damping coefficient. Matched asymptotic expansions are used to study relaxation oscillations for larger values of the damping coefficient. The influence of the powers of the restoring and damping force on the properties of these oscillations is investigated.
Van der Pol oscillator, fractional powers, Krylov-Bogoliubov method, limit cycle, relaxation oscillations
9780854329106
University of Southampton
Kovacic, I.
0cc9489a-2da3-418d-8908-6a902809ef3b
Brennan, M.J.
Kovacic, Ivana
Lopes Jr, V.
Murphy, K.
Petersson, B.
Rizzi, S.
Yang, T.
Kovacic, I.
0cc9489a-2da3-418d-8908-6a902809ef3b
Brennan, M.J.
Kovacic, Ivana
Lopes Jr, V.
Murphy, K.
Petersson, B.
Rizzi, S.
Yang, T.

Kovacic, I. (2010) On the motion of a generalized Van der Pol oscillator: influence of the fractional-order restoring and damping force. Brennan, M.J., Kovacic, Ivana, Lopes Jr, V., Murphy, K., Petersson, B., Rizzi, S. and Yang, T. (eds.) In Proceedings of the Tenth International Conference on Recent Advances in Structural Dynamics (RASD2010). University of Southampton..

Record type: Conference or Workshop Item (Paper)

Abstract

A generalized van der Pol oscillator is considered, with the positive real power nonlinearities in the restoring and damping force, including fractional powers. An analytical approach based on the Krylov–Bogoliubov method is utilized to derive approximate expressions for the amplitude of a limit cycle for small values of the damping coefficient. Matched asymptotic expansions are used to study relaxation oscillations for larger values of the damping coefficient. The influence of the powers of the restoring and damping force on the properties of these oscillations is investigated.

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More information

Published date: 2010
Additional Information: Paper No.130,12pp(Format - USB Pen Drive)
Keywords: Van der Pol oscillator, fractional powers, Krylov-Bogoliubov method, limit cycle, relaxation oscillations

Identifiers

Local EPrints ID: 160737
URI: http://eprints.soton.ac.uk/id/eprint/160737
ISBN: 9780854329106
PURE UUID: a54bef80-ec8b-4747-bca8-8c807efdbc2d

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Date deposited: 21 Jul 2010 07:48
Last modified: 18 Jun 2020 16:32

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