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A Smooth and Discontinuous OscillatorExtended Averaging Method

A Smooth and Discontinuous Oscillator: Extended Averaging Method [This chapter aims at studying the periodic solutions and the Hopf bifurcations of the SD oscillator using the so-called averaging method. This will be done in the case where the system has a viscous damping and an external harmonic excitation. A four dimensional averaging method is introduced by using the complete Jacobian elliptic integrals, directly to obtain the perturbed primary responses which bifurcate from both the hyperbolic saddle point and the non-hyperbolic centers of the unperturbed system. The stability of these periodic solutions is obtained by examining the four dimensional averaged equation using Lyapunov method.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Smooth and Discontinuous OscillatorExtended Averaging Method

Part of the Springer Tracts in Mechanical Engineering Book Series
Cao, Qingjie; Léger, Alain
Springer Journals — Sep 28, 2016
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17 pages

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Publisher
Springer Berlin Heidelberg
Copyright
© Springer-Verlag Berlin Heidelberg 2017
ISBN
978-3-662-53092-4
Pages
103 –120
DOI
10.1007/978-3-662-53094-8_8
Publisher site
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Abstract

[This chapter aims at studying the periodic solutions and the Hopf bifurcations of the SD oscillator using the so-called averaging method. This will be done in the case where the system has a viscous damping and an external harmonic excitation. A four dimensional averaging method is introduced by using the complete Jacobian elliptic integrals, directly to obtain the perturbed primary responses which bifurcate from both the hyperbolic saddle point and the non-hyperbolic centers of the unperturbed system. The stability of these periodic solutions is obtained by examining the four dimensional averaged equation using Lyapunov method.]

Published: Sep 28, 2016

Keywords: Hopf Bifurcation; External Harmonic Excitation; Periodic Solutions; Hyperbolic Saddle Point; Discontinuous Case

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