An oscillator where the restoring force is furnished by a viscoelastic bar and therefore depends on the history of the motion is considered. The history-dependent force is characterized by a relaxation modulus and a relaxation time. Assuming that the relaxation time is small, an approximate model for the oscillator is derived. This model is then linearized for the study of small vibrations. It is shown that the viscoelastic force, in addition to viscous damping, effects an apparent decrease in mass that modifies the natural frequency of the linear oscillator. The temperature dependence of the relaxation time, and consequently the frequency shift, is studied.
Approximate Model for a Viscoelastic Oscillator
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Mar. 20, 2000; final revision, Apr. 24, 2003. Associate Editor: B. M. Moran. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Ketema, Y. (October 10, 2003). "Approximate Model for a Viscoelastic Oscillator ." ASME. J. Appl. Mech. September 2003; 70(5): 757–761. https://doi.org/10.1115/1.1607355
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