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Dr. Khalil Mohamed Khalil Mohamed :: Publications:

Title:
Saddle-node bifurcation control for an odd non-linearity problem.
Authors: A. M. Elnaggar; A. F. El-Bassiouny ; K. M. Khalil
Year: 2011
Keywords: nonlinear system; bifurcation control; saddle-node bifurcation; multiple scales; feedback control.
Journal: Global J. of Pure and Applied Mathematics
Volume: 7
Issue: 2
Pages: 213-229
Publisher: Not Available
Local/International: International
Paper Link: Not Available
Full paper Khalil Mohamed Khalil Mohamed_14_5443 GJPAM__pp 213-229.pdf
Supplementary materials Not Available
Abstract:

The saddle-node bifurcation may occur in the frequency response curves in the cases of primary and superharmonic resonances of a forced single-degree-offreedom (SDOF) nonlinear system. The appearance of this discontinuous or catastrophic bifurcation may lead to jump and hysteresis phenomena in the steady-state response, where at a certain interval of the control parameter, two stable attractors exit with an unstable one in between. In this paper, a feedback control law is designed to control the saddle-node bifurcation taking place in the resonance response, thus removing or delaying the occurrence of jump and hysteresis phenomena. The structure of feedback control law is determined by analyzing the eigenvalues of the modulation equations. It is shown that three types of feedback linear, nonlinear or a combination of linear plus nonlinear are adequate for the bifurcation control. Also, it is shown by illustrative examples that the proposed feedback control law is effective for controlling the primary resonance responses.

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