Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-11T03:38:02.816Z Has data issue: false hasContentIssue false

Performance of a Non Linear Dynamic Vibration Absorbers

Published online by Cambridge University Press:  13 November 2014

F. Djemal*
Affiliation:
Laboratory of Mechanics, Modeling and Manufacturing, National School of Engineers of Sfax, Sfax, Tunisia Engineering Laboratory of Mechanical Systems and Materials, Higher Institute of Mechanics of Paris, Paris, France
F. Chaari
Affiliation:
Laboratory of Mechanics, Modeling and Manufacturing, National School of Engineers of Sfax, Sfax, Tunisia
J.-L. Dion
Affiliation:
Engineering Laboratory of Mechanical Systems and Materials, Higher Institute of Mechanics of Paris, Paris, France
F. Renaud
Affiliation:
Engineering Laboratory of Mechanical Systems and Materials, Higher Institute of Mechanics of Paris, Paris, France
I. Tawfiq
Affiliation:
Engineering Laboratory of Mechanical Systems and Materials, Higher Institute of Mechanics of Paris, Paris, France
M. Haddar
Affiliation:
Laboratory of Mechanics, Modeling and Manufacturing, National School of Engineers of Sfax, Sfax, Tunisia
*
* Corresponding author (fathidjemal@yahoo.fr)
Get access

Abstract

The most common method of vibration control is the use of the dynamic absorbers. Two types of absorbers can be found: Linear and nonlinear. The use of linear absorbers allows reducing vibration but only at the resonance frequency, whereas nonlinear absorbers attenuate vibration on a wide band of frequency. In this paper, a nonlinear two degrees of freedom (DOF) model is developed. A cubic nonlinearity induced by a gap is considered. The objective of the paper is to characterize nonlinear vibration of the system by applying explicit formulation (EF). An experimental study is performed to validate the numerical results. The jump phenomenon is the principal nonlinear dynamic phenomenon observed on both numerical and experimental investigations.

Type
Research Article
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Frahm, H., "Device for Damped Vibrations of Bodies," U.S. Patent No. 989958, Washington, DC: U.S. Patent and Trademark Office (1909).Google Scholar
2.Ormondroyd, J. and DenHartog, J. P., "The Theory of the Dynamic Vibration Absorber," Transactions of ASME, 49, pp. A9A22 (1928).Google Scholar
3.Hunt, J. B., Dynamic Vibration Absorbers, Mechanical Engineering Publications, London, England (1979).Google Scholar
4.Hunt, J. B. and Nissen, J. C., "The Broad Band Dynamic Vibration Absorber," Journal of Sound and Vibration, 83, pp. 573578 (1982).Google Scholar
5.Nissen, J. C., Popp, K. and Schmalhorst, B., "Optimization of a Non-Linear Dynamic Vibration Absorber," Journal of Sound and Vibration, 99, pp. 149154 (1985).Google Scholar
6.Jordanov, I. N. and Cheshankov, B. I., "Optimal Design of Linear and Nonlinear Dynamic Vibration Absorbers," Journal of Sound and Vibration, 123, pp. 157170 (1988).Google Scholar
7.Soom, A. and Lee, M., "Optimal Design of Linear and Non-Linear Vibration Absorbers for Damped Systems," Journal of Vibration, Acoustics, Stress, and Reliability in Design, 105, pp. 112119 (1983).Google Scholar
8.Liu, K. F. and Liu, J., "The Damped Dynamic Vibration Absorbers: Revisited and New Result," Journal of Sound and Vibration, 284, pp. 11811189 (2005).Google Scholar
9.Zhu, S. J., Zheng, Y. F. and Fu, Y. M., "Analysis of Nonlinear Dynamics of a Two-Degree-Of-Freedom Vibration System with Non-Linear Damping and Nonlinear Spring," Journal of Sound and Vibration, 271, pp. 1524 (2004).Google Scholar
10.Hunt, J. B. and Nissen, J. C., "The Broad Band Dynamic Vibration Absorber," Journal of Sound and Vibration, 83, pp. 573578 (1982).Google Scholar
11.Nissen, J. C., Popp, K. and Schmalhorst, B., "Optimization of a Non Linear Dynamic Vibration Absorber," Journal of Sound and Vibration, 99, pp. 149154 (1985).Google Scholar
12.Rice, H. J. and McCraith, J. R., "On Practical Implementations of the Nonlinear Vibration Absorber," Journal of Sound and Vibration, 110, pp. 161163 (1986).CrossRefGoogle Scholar
13.Bert, C. W., Egle, D. M. and Wilkins, D. J., "Optimal Design of a Nonlinear Dynamic Absorber," Journal of Sound and Vibration, 137, pp. 347352 (1990).Google Scholar
14.Rice, H. J., "Combinational Instability of the Non-Linear Vibration Absorber," Journal of Sound and Vibration, 108, pp. 526532 (1986).Google Scholar
15.Natsiavas, S., "Steady State Oscillations and Stability of Non-Linear Dynamic Vibration Absorbers," Journal of Sound and Vibration, 156, pp. 227245 (1992).Google Scholar
16.Siller, H. R. E., "Nonlinear modal analysis methods for engineering structures," Ph.D. Dissertation, Department of Mechanical Engineering, Imperial College London / University of London, U. K. (2004).Google Scholar
17.Kim, T. C., Rook, T. E. and Singh, R., "Effect of Smoothening Functions on the Frequency Response of an Oscillator with Clearance Non-Linearity," Journal of Sound and Vibration, 263, pp. 665678 (2003).Google Scholar
18.Meirovitch, L., Fundamentals of Vibrations, McGraw-Hill, New York, U. S. (2001).Google Scholar