 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13025 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8110
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| In English (Mech. Solids): | | 4915 |
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| M.V. Shitikova and K.A. Modestov, "Analysis of Harmonic Wave Propagation in Fractional Derivative Viscoelastic Media Based on Time-Dependent Modulus of the P-Wave," Mech. Solids. 59 (8), 3949-3967 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
8 |
Pages |
3949-3967 |
| DOI |
10.1134/S0025654424607079 |
| Title |
Analysis of Harmonic Wave Propagation in Fractional Derivative Viscoelastic Media Based on Time-Dependent Modulus of the P-Wave |
| Author(s) |
M.V. Shitikova (Moscow National Research University of Civil Engineering, Moscow, 129337 Russia, ShitikovaMV@mgsu.ru)
K.A. Modestov (Moscow National Research University of Civil Engineering, Moscow, 129337 Russia; Voronezh State Technical University, Voronezh, 394006 Russia, ModestovKA@mgsu.ru) |
| Abstract |
In the present paper, harmonic waves propagating in 3D isotropic viscoelastic media are
analyzed using the fractional derivative Scott-Blair model, Kelvin-Voigt model, Maxwell model and
standard linear solid model. It is known that only the first and second Lamé constants, or the bulk and
shear moduli, appear in Hooke’s law for three-dimensional media, but not Young’s modulus or Poisson’s ratio. This indicates that the bulk and Lamé operators are the most intrinsic operators to express
stress in terms of strain when studying wave propagation in 3D viscoelastic media. That is why in the
present paper, the emphasis is made on the comprehensive analysis of time-dependent operators for
Lamé parameters. In so doing, the fractional derivative models are utilized for defining the time-dependent modulus of the P-wave, which governs the velocity of the longitudinal wave. Asymptotic
values of the wave velocities, their coefficients of attenuation and logarithmic decrements have been found for the case of absence of bulk relaxation. |
| Keywords |
viscoelastic media, rheological models, fractional derivative, logarithmic decrement of attenuation, dispersion, time-dependent P-wave modulus |
| Received |
15 December 2024 | Revised |
29 December 2024 | Accepted |
30 December 2024 |
| Link to Fulltext |
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