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Influence of the Internal State of a Maxwell Damper on Free Critically Damped Vibrations

[+] Author and Article Information
M. B. Rubin

Faculty of Mechanical Engineering,
Technion—Israel Institute of Technology,
Haifa 32000, Israel
e-mail: mbrubin@tx.technion.ac.il

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received November 22, 2012; final manuscript received March 11, 2013; published online June 19, 2013. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 135(6), 064503 (Jun 19, 2013) (5 pages) Paper No: VIB-12-1324; doi: 10.1115/1.4024054 History: Received November 22, 2012; Revised March 11, 2013

A Maxwell damper with a damper spring in series with a viscous dashpot is a more physical model than a viscous dashpot because the Maxwell damper models the elasticity of the connecting links of the viscous dashpot. The system of a main spring in parallel with a Maxwell damper is known as the standard linear solid (SLS) in viscoelasticity. The response of this SLS attached to a mass for standard initial value problems: displacement (nonzero displacement with zero velocity) and velocity (zero displacement with nonzero velocity) have been analyzed a few times in the literature. However, different authors present different conclusions about the importance of modeling the damper spring. None of these authors have explored the influence of the initial internal state of the damper spring. Here it is shown that the initial internal state of the damper spring can significantly influence the response for both displacement and velocity initial value problems.

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References

Crandall, S. H., 1970, “The Role of Damping in Vibration Theory,” J. Sound Vib., 11, pp. 3–18. [CrossRef]
Christensen, R. M., 1971, Theory of Viscoelasticity, Academic Press, New York.
Flugge, W., 1975, Viscoelasticity, Springer-Verlag, Berlin.
Gallagher, J., and Volterra, E., 1952, “A Mathematical Analysis of the Relaxation Type of Vehicle Suspension,” ASME J. Appl. Mech., 74, pp. 389–396.
Yamakawa, I., 1961, “On the Free Vibration and the Transient State of One-Degree-of-Freedom System With Elastically Supported Damper,” Bull. JSME4, pp. 641–644. [CrossRef]
Ruzicka, J. E., 1967, “Resonance Characteristics of Unidirectional Viscous and Coulomb-Damped Vibrational Isolation Systems,” ASME J. Eng. Ind., 89, pp. 729–740. [CrossRef]
Derby, T. F., and Calcaterra, P. C., 1970, “Response and Optimization of an Isolator With Relaxation Type Damping,” Shock Vib. Bull., 40, pp. 203–216.
Muravyov, A., and Hutton, S. G., 1998, “Free Vibration Response Characteristic of a Simple Elasto-Hereditary System,” ASME, J. Vib. Acoust., 120, pp. 628–632. [CrossRef]
AdhikariS., 2002, “Dynamics of Nonviscously Damped Linear Systems,” J. Eng. Mech., 128, pp. 328–339. [CrossRef]
Muller, P., 2005, “Are the Eigensolutions of a 1-D.O.F. System With Viscoelastic Damping Oscillatory or Not?,” J. Sound Vib., 285, pp. 501–509. [CrossRef]
Brennan, M. J., Carrella, A., Walters, T. P., and Lopes, V., Jr., 2008, “On the Dynamic Behaviour of a Mass Supported by a Parallel Combination of a Spring and an Elastically Connected Damper,” J. Sound Vib., 309, pp. 823–837. [CrossRef]
Dimarogonas, A. D., and Haddad, S., 1992, Vibrations for Engineers, Prentice-Hall, Englewood Cliffs, NJ.
Shimizu, K., Yamada, T., Tagami, J., and Kurino, H., 2004, “Vibration Tests of Actual Buildings With Semi-Active Switching Oil Damper,” Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, BC, Canada, August 1–6, Paper No. 153.
Suciu, C. V., Tobiishi, T., and Mouri, R., 2012, “Modeling and Simulation of a Vehicle Suspension With Variable Damping Versus the Excitation Frequency,” J. Telecommun. Inf. Technol., 1, pp. 83–89. [CrossRef]
Makris, N., Dargush, G. F., and Constantinou, M. C., 1993, “Dynamic Analysis of Generalized Viscoelastic Fluids,” ASCE J. Struct. Eng., 119, pp. 1663–1679. [CrossRef]
Rossikhin, Y. A., Shitikova, M. V., and Shcheglova, T., 2009, “Forced Vibrations of a Nonlinear Oscillator With Weak Fractional Damping,” J. Mech. Mater. Struct., 4, pp. 1619–1636. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Sketch of a mass m connected to a fixed wall by a main spring {ks,L0} and a Maxwell damper {kd,cd}

Grahic Jump Location
Fig. 5

Velocity solution: Influence of the initial internal state of the Maxwell damper (A0 in Eq. (4.15)) for different normalized stiffnesses κd of the damper spring and for the two critical values {ζc1, ζc2}. Comparison with the prediction ev of the standard dashpot model.

Grahic Jump Location
Fig. 4

Displacement solution: Influence of the initial internal state of the Maxwell damper (A0 in Eq. (4.15)) for different normalized stiffnesses κd of the damper spring and for the two critical values {ζc1, ζc2}. Comparison with the prediction ev of the standard dashpot model.

Grahic Jump Location
Fig. 3

Velocity solution: Influence of the normalized stiffness κd of the damper spring on the solution for both critical values {ζc1, ζc2} of damping. Comparison with the prediction ev of the standard dashpot model.

Grahic Jump Location
Fig. 2

Displacement solution: Influence of the normalized stiffness κd of the damper spring on the solution for both critical values {ζc1, ζc2} of damping. Comparison with the prediction ev of the standard dashpot model.

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