Oscillations of a viscoelastic medium with a cylindrical cavity are studied. The viscosity is taken into account in the form of an additional term in the constitutive equation, proportional to a fractional derivative of variable order. In the considered examples the order function corresponds to dependences obtained for real materials. A damping effect is observed in the amplitude behavior. The field which determines the order function demonstrates the viscoelastic behavior of the material under load.
Application of Dynamic Fractional Differentiation to the Study of Oscillating Viscoelastic Medium With Cylindrical Cavity
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 2001; revised March 2002. Associate Editor: L. A. Bergman.
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Ingman , D., and Suzdalnitsky, J. (September 20, 2002). "Application of Dynamic Fractional Differentiation to the Study of Oscillating Viscoelastic Medium With Cylindrical Cavity ." ASME. J. Vib. Acoust. October 2002; 124(4): 642–645. https://doi.org/10.1115/1.1497364
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