VIBRATION SUPRESSION OF NON-LINEAR SYSTEM VIA NON-LINEAR ABSORBER | ||
| Menoufia Journal of Electronic Engineering Research | ||
| Article 5, Volume 17, Issue 1, January 2007, Pages 59-77 | ||
| Document Type: Original Article | ||
| DOI: 10.21608/mjeer.2007.65201 | ||
| Authors | ||
| Y.A. Amer1; A.T. EL-Sayed2 | ||
| 1Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt | ||
| 2Department of Basic Sciences, Modern Academy for Engineering and Technology,Egypt | ||
| 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. | ||
| References | ||
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[1] Elnaschie MS. Stress, stability and chaos. Mc Graw-Hill International Editions (1992). Singapore. Copyright (1990) Mc Graw HillUnited Kingdom.
[2] Oueini SS, Nayfeh AH, Single-Mode control of a cantilever beam under principal parametric excitation, Journal of Sound and Vibration 224(1) (1999) 33-47
[3] Amer YA, "On the solution of parametrically excited different systems of non-linear differential equations", the Ph.D. Thesis, Department of Mathematics, Faculty of Science, Zagazig University, Egypt (2002)
[4] El-Bassiouny AF, Eissa M, Dynamics of a single-degree-of-freedom structure with quadratic, cubic and quartic non-linearities to a harmonic resonance, Applied Mathematics and Computation 139 (2003) 1-21
[5] Song Y, Sato H, Iwata Y and Komatsuzaki T, The response of a dynamic vibration absorber system with a parametrically excited pendulum, Journal of Sound and Vibration 259 (4) (2003) 747-759
[6] Zhu SJ, Zheng YF, Fu YM, Analysis of non-linear dynamics of a two-degree-of-freedom vibration system with non-linear damping and non-linear spring, Journal of Sound and Vibration 271 (2004) 15-24
[7] Lim FCN, Cartmell MP, Cardoni A, Lucas M, A preliminary investigation into optimising the response of vibrating systems used for ultrasonic cutting, Journal of Sound and Vibration 272 (2004) 1047-1069
[8] Eissa M. , Amer YA, Vibration control of a cantilever beam subject to both external and parametric excitation, Applied Mathematics and Computation 152 (2004) 611-619
[9] Eissa M,EL-Ganaini WAA, Hamed YS, Saturation, stability and resonance of non-linear systems, Physica A 356 (2005) 341-358
[10] Eissa M,EL-Ganaini WAA, Hamed YS, Scientific Bulletin, Part III : Mechanical Engineering and Physics & Mathematics ,faculty of engineering (Ain Shams university) 40 (1) (2005) 1113-1127
[11] Eissa M,EL-Ganaini WAA, Hamed YS, On the Saturation Phenomena and Resonance of non-linear differential equations, Minufiya Journal of Electronic Engineering Research MJEER 15 (1) (2005) 73-84
[12] Nayfeh AH, Resolving Controversies in the Application of the Method of Multiple Scales and the Generalized Method of Averaging, Nonlinear Dynamics 40 (2005) 61-102
[13] EL-Bassiouny AF, Effect of non-linearities in elastomeric material dampers on torsional oscillation control, Applied Mathematics and Computation 162 (2005) 835-854
[14] Eissa M, Sayed M, A Comparison between active and passive vibration control of non-linear simple pendulum, Part I : Transversally tuned absorber and negative Gⁿ feedback, Mathematical and Computational Applications 11 (2) (2006) 137-149
[15] Eissa M, Sayed M, A Comparison between active and passive vibration control of non-linear simple pendulum, Part II : Longitudinal tuned absorber G and negative Gⁿ feedback, Mathematical and Computational Applications 11 (2) (2006) 151-162
[16] Amer YA, Vibration control of ultrasonic cutting via dynamic absorber, Accepted for publication in Chaos, Solitons & Fractals | ||
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