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Vibration and chaos control of non-linear torsional vibrating systems

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  • El-Bassiouny, A.F.

Abstract

Vibration of a mechanical system is often an undesirable phenomenon, as it may cause damage, disturbance, discomfort and, sometimes, destruction of systems and structures. To reduce vibration, many methods can be used. The most famous method is using dynamic absorbers or dampers. In the present work, a non-linear elastomeric damper or absorber is used to control the torsional vibrations of the crankshaft in internal combustion engines, when subjected to both external and parametric excitation torques. The multiple time scale perturbation method is applied to determine the equations governing the modulation of both amplitudes and phases of the crankshaft and the absorber. These equations are used to determine the steady-state amplitudes and system stability. Numerical integration of the basic equations is applied to investigate the effects of the different parameters on system behavior. A comparison is made with the available published work. Some recommendations are given at the end of the work.

Suggested Citation

  • El-Bassiouny, A.F., 2006. "Vibration and chaos control of non-linear torsional vibrating systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 167-186.
    • Handle: RePEc:eee:phsmap:v:366:y:2006:i:c:p:167-186
    DOI: 10.1016/j.physa.2005.10.049
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    References listed on IDEAS

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    1. El-Bassiouny, A.F. & Kamel, M.M. & Abdel-Khalik, A., 2003. "Two-to-one internal resonances in nonlinear two degree of freedom system with parametric and external excitations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(1), pages 45-56.
    2. El-Bassiouny, A.F. & Abdelhafez, H.M., 2001. "Prediction of bifurcations for external and parametric excited one-degree-of-freedom system with quadratic, cubic and quartic non-linearities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(1), pages 61-80.
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    Cited by:

    1. EL-Sayed, A.T. & Bauomy, H.S., 2022. "NIPPF versus ANIPPF controller outcomes on semi-direct drive cutting transmission system in a shearer," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Jiang, Song & Li, Wei & Xin, Gaifang & Sheng, Lianchao & Fan, Mengbao & Yang, Xuefeng, 2020. "Analysis of torsional vibration characteristics and time delay feedback control of semi-direct drive cutting transmission system in shearer," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. El-Bassiouny, A.F., 2009. "On methods for continuous systems with quadratic, cubic and quantic nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1308-1316.

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