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Bifurcation Phenomena Caused by Two Nonlinear Dynamic Absorbers

[+] Author Affiliations
Takashi Ikeda

Shimane University, Matsue, Shimane, Japan

Paper No. DETC2007-34714, pp. 1653-1661; 9 pages
doi:10.1115/DETC2007-34714
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

The characteristics of two nonlinear vibration absorbers simultaneously attached to structures under harmonic excitation are investigated. The frequency response curves are theoretically determined using van der Pol’s method. It is found from the theoretical analysis that pitchfork bifurcations may appear on a part of the response curves which are stable in a system with one nonlinear dynamic absorber. Three steady-state solutions with different amplitudes appear just after the pitchfork bifurcation. After that, Hopf bifurcations may occur depending on the values of the system parameters, and amplitude- and phase-modulated motion including a chaotic vibration appears after the Hopf bifurcation. Lyapunov exponents are numerically calculated to prove the occurrence of a chaotic vibration. In addition, it is also found that only Hopf bifurcations, not pitchfork bifurcations, can occur even when the linear and nonlinear dynamic absorbers are combined.

Copyright © 2007 by ASME
Topics: Bifurcation

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