Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

IMPACT FACTOR 2017: 1.414

CiteScore 2018: 1.15

SCImago Journal Rank (SJR) 2018: 0.370
Source Normalized Impact per Paper (SNIP) 2018: 0.431

See all formats and pricing
More options …
Volume 61, Issue 10-11


The Response of Nonlinear Single-Degree-of-Freedom Systems to Modulated High-Frequency Input

Atef F. El-Bassiouny
  • Faculty of Science, Mathematics Department, Benha University, Benha 13518, Egypt Present address: P. O. Box 3137, Quassim, Onaizah, Kingdom of Saudi Arabia
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-06-02 | DOI: https://doi.org/10.1515/zna-2006-10-1105

In this paper we study the response of single-degree-of-freedom with cubic, quartic and quintic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contains frequencies much lower than the carrier frequency of the excitation. The method of multiple scales is used to derive two coupled first-order ordinary differential equations that describe the evolution of the amplitude and phase with damping, nonlinearities and resonances. The evolution equations are used to determine the steady-state motions, while representative frequency-response curves are presented for each resonance. Stability analysis of the amplitude and phase modulation equations for both cases are performed. The bending of the response curves leads to multi-valued solutions and hence to jump phenomena.

Keywords : Nonlinear Oscillations; Modulation Equations; Resonances; Carrier Frequency; Fixed Points; Stability

About the article

Received: 2005-09-22

Published Online: 2014-06-02

Published in Print: 2006-11-01

Citation Information: Zeitschrift für Naturforschung A, Volume 61, Issue 10-11, Pages 541–555, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2006-10-1105.

Export Citation

© 1946 – 2014: Verlag der Zeitschrift für Naturforschung. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in