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Localization Phenomena in Pendulum Arrays Subjected to Vertical Excitation

[+] Author Affiliations
Takashi Ikeda, Yuji Harata, Chongyue Shi, Keisuke Nishimura

Hiroshima University, Higashi-Hiroshima, Hiroshima, Japan

Paper No. DETC2014-34461, pp. V006T10A054; 10 pages
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4639-1
  • Copyright © 2014 by ASME


Localization phenomena, also referred to as intrinsic localized modes (ILMs), are investigated in an N-pendulum array subjected to vertical harmonic excitation. The pendula behave nonlinearly and are connected with each other by weak linear springs. In the theoretical analysis, van der Pol’s method is employed to determine the expressions for frequency response curves for the principal parametric resonances, considering the nonlinear restoring moment of the pendula. In the numerical results, frequency response curves for N=2 and 3 are shown to examine the patterns of ILMs, and the influences of the connecting spring constants and the imperfections of the pendula. Bifurcation sets are also calculated to show the excitation frequency range and the conditions for the occurrence of ILMs. Increasing the connecting spring constant results in the appearance of Hopf bifurcation. The numerical simulations reveal the occurrence of ILMs with amplitude modulated motions (AMMs) including chaotic motions. ILMs were observed in experiments, and the experimental data were compared with the theoretical results. The validity of the theoretical analysis was confirmed by the experimental data.

Copyright © 2014 by ASME
Topics: Pendulums



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