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Journal of Applied Nonlinear Dynamics 3(4) (2014) 359--368 | DOI:10.5890/JAND.2014.12.007

Jaros law Dyk; Adam Jungowski; Jerzy Osiński

Warsaw University of Technology, Institute of Machine Design Fundamentals, ul. Narbutta 84, 02-524, Warsaw, Poland

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Abstract

The main focus of interest in the report is the specific irregular character of the motion in the system with an elastomeric element being a part of the frictional damper. The solution to this problem is based on the assumption that the material of the elastomeric element is non-compressible and its properties are described by Mooney-Rivlin model of the first order. Additionally, the values of the coefficients are chosen on the basis of the experiments described in references. The form of the equation of motion, which has been written by use of the non-compressiblity condition, testifies that vibrations of the system have the strong non-linear character. The numerical calculations by use of Gear's method, have given the evidence that after more than ten thousands of periods the irregular motion is present. For the case of the calculation of dissipative energy by acting dry friction between the elastomer and an aluminum element, as well as by the viscous damping, the equation of motion has been supplemented with suitable elements. It has been affirmed that the irregular motion is present only in the case of the system that exhibits the low level of damping. The detailed experiment research work on the elastomeric friction damper, in the frequency range up to 10Hz and different levels of temperature, confirms the strongly non-linear character of the motion.

Acknowledgments

The main thesis of this paper were presented during 12th Conference on Dynamical Systems- Theory and Applications [8].

References

1. [1]	Boczkowska, A., Babski, K., Osiński, J. and Żach P. (2008), Identification of viscoelastic properties of hiperelastic materials, Polimery, nr 7/8, 53, 554-550 (in Polish).

2. [2]	Żach, P. (2013), Structural identification of the spring and damping quality for hyperelastic material, ITER, Radom, (in Polish).

3. [3]	Ward, I.M. (1971), Mechanical Properties of Solid Polymers, Wiley, New York.

4. [4]	Damping of Vibration, (1998), (Edited by Osi ski, Z.), A.A. Balkema/ Rotterdam/ Brookfield/.

5. [5]	Dyk, J. (2006), Chaotic Vibrations in a model of two-stage Gear, Proceeding of the XI International Conference "Computer Simulation in Machine Design"- COSIM2006, Krynica Zdrój, Poland, 30 August-1 September, 116-124.

6. [6]	Dyk, J. , Krupa, A. and Osiński, J. (1994), Analysis of Chaos in Systems with Gears, Journal of Theoretical and Applied Mechanics, 32(3), 549-556.

7. [7]	Schuster, H.G., (1988), Deterministic Chaos. An Introduction, Second revised edition, VCH Verlagsgesellschaft, Weinheim.

8. [8]	Dyk, J., Jungowski, A., and Osiński, J. (2013), Irregular motion in the vibration systems with an elastomeric friction element, (in: DYNAMICAL SYSTEMS- Applications, Editors: Awrejcewicz, J., Kaźmierczak , M., Olejnik, P. and Mrozowski, J.), Lódź, December 2-5, Poland, 365-374.