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Suppression of nonlinear vibration system described by nonlinear differential equations using passive controller

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Abstract

In this paper, the linear absorber is proposed to reduce the vibration of a nonlinear dynamical system at simultaneous primary resonance and the presence of 1:1 internal resonance. This leads to a two-degree-of-freedom system subjected to external excitation force. The method of multiple scales perturbation technique is applied throughout to determine the analytical solution up to first-order approximations. The stability of the system near the one of the worst resonance case is studied using the frequency response equations. The effects of the different system and absorber parameters on the behavior of the main system are studied numerically. For validity, the numerical solution is compared with the analytical solution and gets a good agreement. Effectiveness of the absorber (\(E_{a})\) is about 800 for the nonlinear vibrating system. The simulation results are achieved using MATLAB programs. At the end of the work, the comparison with the available published work is reported.

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Acknowledgments

The author would like to thank the reviewers for their valuable comments and suggestions for improving the quality of this paper.

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Authors and Affiliations

  1. Department of Basic Sciences, Modern Academy for Engineering and Technology, Cairo, Egypt

    A. T. EL-Sayed

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  1. A. T. EL-Sayed
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Correspondence to A. T. EL-Sayed.

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EL-Sayed, A.T. Suppression of nonlinear vibration system described by nonlinear differential equations using passive controller. Nonlinear Dyn 78, 1683–1694 (2014). https://doi.org/10.1007/s11071-014-1550-7

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  • DOI: https://doi.org/10.1007/s11071-014-1550-7

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