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M. Sayed, Y. S. Hamed and Y. A. Amer, “Vibration Reduction and Stability of Non-Linear System Subjected to External and Parametric Excitation Forces under a Non- linear Absorber,” International Journal of Contemporary Mathematical Sciences, Vol. 6, No. 22, 2011, pp. 1051-1070.

has been cited by the following article:

• TITLE: The Analytical and Numerical Solutions of Differential Equations Describing of an Inclined Cable Subjected to External and Parametric Excitation Forces

  AUTHORS: Mohamed S. Abd Elkader

  KEYWORDS: Perturbation Method, Resonance, Chaotic Response, Stability

  JOURNAL NAME: Applied Mathematics, Vol.2 No.12, December 27, 2011

  ABSTRACT: The analytical and numerical solutions of the response of an inclined cable subjected to external and parametric excitation forces is studied. The method of perturbation technique are applied to obtained the periodic response equation near the simultaneous principal parametric resonance in the presence of 2:1 internal resonance of the system. All different resonance cases are extracted. The effects of different parameters and worst resonance case on the vibrating system are investigated. The stability of the system are studied by using frequency response equations and phase-plane method. Variation of the parameters α2, α3, β2, γ2, η2, γ3, η3, f2 leads to multi-valued amplitudes and hence to jump phenomena. The simulation results are achieved using MATLAB 7.6 programs.