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

Author(s)
Mohamed S. Abd Elkader

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.

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.

Cite this paper

nullM. Elkader, "The Analytical and Numerical Solutions of Differential Equations Describing of an Inclined Cable Subjected to External and Parametric Excitation Forces,"*Applied Mathematics*, Vol. 2 No. 12, 2011, pp. 1469-1478. doi: 10.4236/am.2011.212209.

nullM. Elkader, "The Analytical and Numerical Solutions of Differential Equations Describing of an Inclined Cable Subjected to External and Parametric Excitation Forces,"

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