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Nonlinear vibration behavior and resonance of a Cartesian manipulator system carrying an intermediate end effector

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Abstract

This paper studied the nonlinear vibration and resonance of a Cartesian manipulator system carrying an intermediate end effector under mixed excitations. The multiple scales method is applied to get the approximate solutions of this system of the second-order differential equation. Furthermore, the analytical solution obtained the amplitudes and phases of the response from the first-order differential equation governing. We extracted all worst resonance cases and studied it numerically. The numerical solutions and response amplitude of this system are also studied and discussed. We analyzed the stability of the steady-state solution of a Cartesian manipulator system using frequency response equations and phase plane technique at the worst resonance cases. Comparison between analytical and numerical solutions is obtained. We determined both bifurcation diagrams and stability using Poincaré maps. Also, the numerical results are obtained using MAPLE and MATLAB algorithms.

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Acknowledgements

The authors thank the anonymous reviewers for their useful comments that improved the quality of the paper.

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Authors and Affiliations

  1. Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf, 32952, Egypt

    Y. S. Hamed

  2. Department of Mathematics and Statistics, Faculty of Science, Taif University, P.O. Box 888, El-Haweiah, Taif, Zip Code 21974, Kingdom of Saudi Arabia

    Y. S. Hamed & M. R. Alharthi

  3. Department of Mathematics, Faculty of Sciences and Home Economics, Bisha University, Bisha, 61922, Kingdom of Saudi Arabia

    H. K. AlKhathami

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  1. Y. S. Hamed
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  2. M. R. Alharthi
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  3. H. K. AlKhathami
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Correspondence to Y. S. Hamed.

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Hamed, Y.S., Alharthi, M.R. & AlKhathami, H.K. Nonlinear vibration behavior and resonance of a Cartesian manipulator system carrying an intermediate end effector. Nonlinear Dyn 91, 1429–1442 (2018). https://doi.org/10.1007/s11071-017-3955-6

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  • DOI: https://doi.org/10.1007/s11071-017-3955-6

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