Definitions
Vibrations of viscoelastic rods of finite length have been considered for the cases, when the viscoelastic features of rods are described by ten rheological models involving several fractional operators of different orders.
Backgrounds
Viscoelastic models containing fractional derivatives of different orders and other fractional operators with more than one independent fractional parameter (the fractional parameter is the order of the fractional derivative or fractional operator) have long attracted the attention of investigators (Rossikhin and Shitikova, 2001). This is due to the fact that such models enable one to vary the rheological parameters in a broad fashion and, more importantly, allow one to obtain the best fit of experimental data to theoretical results (Rossikhin and Shitikova, 2004).
The generalization of the classical stress-strain relations describing...
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References
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Rossikhin, Y.A., Shitikova, M.V. (2019). Vibrations of Viscoelastic Rods, Fractional Operator Models. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_81-1
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DOI: https://doi.org/10.1007/978-3-662-53605-6_81-1
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