VIBRATION SUPRESSION OF NON-LINEAR SYSTEM VIA NON-LINEAR ABSORBER

Amer, Y.A.; EL-Sayed, A.T.

doi:10.21608/mjeer.2007.65201

VIBRATION SUPRESSION OF NON-LINEAR SYSTEM VIA NON-LINEAR ABSORBER

Document Type : Original Article

Authors

Y.A. Amer ¹
A.T. EL-Sayed ²

¹ Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

² Department of Basic Sciences, Modern Academy for Engineering and Technology,Egypt

10.21608/mjeer.2007.65201

Abstract

In this paper, the coupled non-linear differential equations of the non-linear dynamical two-degree-of-freedom vibrating system including quadratic and cubic non-linearities are studied. The system consists of the main system and the absorber. The absorber is used to control the main system vibrations when subjected to multi external excitation forces at simultaneous primary and internal resonance. The method of multiple scales perturbation technique (MSPT) is applied throughout to determine the solution up to third order approximations. The different resonance cases are reported and studied numerically. Stability is studied applying frequency response functions. The effect of different parameters of the system are studied numerically. A comparison is made with the available published work.

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