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JOURNALS // Izvestiya of Saratov University. Mathematics. Mechanics. Informatics // Archive

Izv. Saratov Univ. Math. Mech. Inform., 2025 Volume 25, Issue 2, Pages 214–230 (Mi isu1078)

Scientific Part
Mechanics

Harmonic wave propagation in viscoelastic media modelled via fractional derivative models

K. A. Modestovab, M. V. Shitikovaa

a Moscow State University of Civil Engineering (National Research University), 26 Yaroslavsckoye Shosse, Moscow 129337, Russia
b Voronezh State Technical University, 84 20-letiya Oktyabrya St., Voronezh 394006, Russia

Abstract: In the present paper, harmonic waves propagating in 3D isotropic viscoelastic media are analyzed using the fractional derivative Kelvin – Voigt model, Maxwell model and standard linear solid model. Asymptotic values of the wave velocities, their coefficients of attenuation and logarithmic decrements have been found.

Key words: viscoelastic media, rheological models, fractional derivative, logarithmic decrement of attenuation, dispersion.

UDC: 517.98

Received: 10.08.2024
Revised: 15.11.2024

DOI: 10.18500/1816-9791-2025-25-2-214-230



© Steklov Math. Inst. of RAS, 2025