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TECHNICAL PAPERS

Approximate Model for a Viscoelastic Oscillator

[+] Author and Article Information
Y. Ketema

Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455

J. Appl. Mech 70(5), 757-761 (Oct 10, 2003) (5 pages) doi:10.1115/1.1607355 History: Received March 20, 2000; Revised April 24, 2003; Online October 10, 2003
Copyright © 2003 by ASME
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References

Okazaki,  A., Urata,  Y., and Tatemichi,  A., 1990, “Damping Properties of a Three Layered Shallow Spherical Shell With a Constrained Viscoelastic Layer,” JSME Int. J., Ser. I, 33(2), pp. 145–151.
Gautham,  B. P., and Ganesan,  N., 1994, “Vibration and Damping Characteristics of Spherical Shells With a Viscoelastic Core,” J. Sound Vib., 170(3), pp. 289–301.
Culkowski,  P. M., and Reismann,  H., 1971, “The Spherical Sandwich Shell Under Axisymmetric Static and Dynamic Loading,” J. Sound Vib., 14, pp. 229–240.
Truesdell, C., and Noll, W., 1965, “The Non-Linear Field Theories of Mechanics,” Handbook of Physics, III/3, Springer, New York.
Coleman,  B. D., 1964, “Thermodynamics of Materials With Memory,” Arch. Ration. Mech. Anal., 17(1), pp. 1–46.
Fosdick,  R. L., Ketema,  Y., and Yu,  J. H., 1998, “Vibration Damping Through the Use of Materials With Memory,” Int. J. Solids Struct., 35, pp. 403–420.
Fosdick,  R. L., and Ketema,  Y., 1998, “A Thermoviscoelastic Dynamic Vibration Absorber,” J. Appl. Mech., 65, pp. 17–24.
Ketema,  Y., 1998, “A Viscoelastic Dynamic Vibration Absorber With Adaptable Suppression Band: A Feasibility Study,” J. Sound Vib., 216(1), pp. 133–145.
Fosdick,  R. J., Ketema,  Y., and Yu,  J. H., 1998, “A Nonlinear Oscillator With History Dependent Forces,” Int. J. Non-Linear Mech., 33, pp. 447–459.
Coleman,  B. D., and Noll,  W., 1960, “An Approximation Theorem for Functionals, With Applications in Continuum Mechanics,” Arch. Ration. Mech. Anal., 6, pp. 355–370.
Nayfeh, A. H., 1973, Perturbation Methods, John Wiley and Sons, New York.
Ferry, J. D., 1970, Viscoelastic Properties of Polymers, 2nd Ed., John Wiley and Sons, New York.
Moore, D. F., 1993, Viscoelastic Machine Elements, Butterworth-Heineman Ltd., Oxford.

Figures

Grahic Jump Location
Schematic diagram of a linear oscillator with history-dependent forces
Grahic Jump Location
Damped natural frequency of a viscoelastic oscillator as a function of the relaxation time: (a) second-order approximation (solid line), (b) first-order approximation, (dashed line). Φ0=1,x̃*=1.
Grahic Jump Location
The variation of the normalized relaxation time with temperature
Grahic Jump Location
The variation of the normalized damped natural frequency with temperature

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