Full Content is available to subscribers

Subscribe/Learn More  >

Approximation of the Frequency-Energy Dependence in the Nonlinear Dynamical Systems

[+] Author Affiliations
Mohammad A. Al-Shudeifat

Khalifa University of Science, Technology & Research, Abu Dhabi, UAE

Paper No. DETC2016-60163, pp. V006T09A042; 7 pages
  • ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Charlotte, North Carolina, USA, August 21–24, 2016
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5018-3
  • Copyright © 2016 by ASME


In this work, a method is introduced for extracting the approximate backbone branches of the frequency-energy plot from the numerical simulation response of the nonlinear dynamical system. The duffing oscillator is firstly considered to describe the method and later a linear oscillator (LO) coupled with a nonlinear energy sink (NES) is also considered for further demonstration. The systems of concern are numerically simulated at an arbitrary high level of initial input energy. Accordingly, the obtained responses of these systems are employed via the proposed method to extract an approximation for the fundamental backbone branches of the frequency-energy plot. The obtained backbones have been found in excellent agreement with the exact backbones of the considered systems. Even though these approximate backbones have been obtained for only one high energy level, they are still valid for any other initial energy below that level. In addition, they are not affected by the damping variations in the considered systems. Unlike other existing methods, the proposed approach is applicable to well-approximate the backbone branches of the large-scale nonlinear dynamical systems.

Copyright © 2016 by ASME



Interactive Graphics


Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature

Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In