Strongly Nonlinear Oscillators Subject to Delay-Reference-Cited by-同舟云学术

Strongly Nonlinear Oscillators Subject to Delay

Published:2010-06 Issue:7-8 Volume:16 Page:1141-1149
ISSN:1077-5463
Container-title:Journal of Vibration and Control
language:en
Short-container-title:Journal of Vibration and Control

Author:

Erneux Thomas¹

Affiliation:

1. Université Libre de Bruxelles, Optique Nonliéaire Théorique, Campus Plaine, C.P. 231, 1050 Bruxelles, Belgium, terneux@ulb.ac.be

Abstract

A large class of strongly nonlinear conservative oscillators subject to a delayed feedback are modeled mathematically by second-order delay differential equations. Recent applications include the control of crane oscillations and lasers subject to optoelectronic feedback. We apply the method of averaging in the case of weak damping and weak feedback and determine the bifurcation diagram of the limit-cycle solutions. We find that the coexistence of a stable equilibrium with one or several stable periodic solutions is unavoidable if the delay is sufficiently large.

Publisher

SAGE Publications

Subject

Mechanical Engineering,Mechanics of Materials,Aerospace Engineering,Automotive Engineering,General Materials Science

Link

http://journals.sagepub.com/doi/pdf/10.1177/1077546309341130

Reference19 articles.

1. The Modulated Phase Shift for Strongly Nonlinear, Slowly Varying, and Weakly Damped Oscillators

2. Averaging Methods for the Phase Shift of Arbitrarily Perturbed Strongly Nonlinear Oscillators with an Application to Capture

3. Erneux, T., 2000, "Multiple time scale analysis of lasers," in Fundamental Issues of Nonlinear Dynamics (AIP Conf. Proc., 548), Krauskopf, B. and Lenstra, D. (eds). American Institute of Physics, New York, p. 54-65.

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