Harmonic longitudinal waves in discretely inhomogeneous viscoelastic rods
https://doi.org/10.22227/1997-0935.2026.2.207-218
Abstract
Introduction. Harmonic longitudinal waves in semi-infinite discretely inhomogeneous viscoelastic rods composed of an arbitrary number of viscoelastic layers are considered. The aim of the study is to develop an analytical solution and to investigate the influence of the properties of layered materials and viscoelastic models on wave dispersion and attenuation, which is important for vibration processes.
Materials and methods. The method is based on the spectral representation of the equations of motion and is applied to the classical models of Kelvin – Voigt, Maxwell, and the Standard Linear Solid (SLS). Explicit complex dispersion relations, expressions for the damping coefficient, and criteria for the sharp increase in amplitude when a wave passes through layer interfaces were obtained.
Results. Dependencies of damping on the elastic modulus, density, relaxation/retardation times.
Conclusions. It is concluded that the proposed analytical approach provides a reliable basis for the targeted design of vibration-isolating metamaterials and seismic barriers with predetermined frequency characteristics.
Keywords
viscoelasticity,
longitudinal waves,
discretely inhomogeneous rods,
harmonic excitations,
Maxwell model,
Kelvin – Voigt model,
standard linear solid model
Supporting agencies: This work (by S.G. Saiyan) was supported by the Russian Science Foundation, Grant No. 24-49-02002.
About the Authors
S. G. Saiyan
Moscow State University of Civil Engineering (National Research University) (MGSU); Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences (IPMech RAS)
Russian Federation
Russian Federation
Sergey G. Saiyan — research fellow at the A.B. Zolotov Scientific and Educational Center for Computer Modeling of Unique Buildings, Structures, and Complexes, senior lecturer at the Department of Structural and Theoretical Mechanics, lecturer at the Department of Computer Science and Applied Mathematics; junior research fellow
26 Yaroslavskoe shosse, Moscow, 129337;
build. 1, 101 Vernadsky ave., Moscow, 119526
RSCI AuthorID: 987238, Scopus: 57195230884, ResearcherID: AAT-1424-2021
A. A. Marasanova
Moscow State University of Civil Engineering (National Research University) (MGSU)
Russian Federation
Russian Federation
Anastasia A. Marasanova — student
26 Yaroslavskoe shosse, Moscow, 129337
K. D. Ivanchenko
Moscow State University of Civil Engineering (National Research University) (MGSU)
Russian Federation
Russian Federation
Ksenia D. Ivanchenko — student
26 Yaroslavskoe shosse, Moscow, 129337
K. A. Modestov
Moscow State University of Civil Engineering (National Research University) (MGSU); Voronezh State Technical University (VSTU)
Russian Federation
Russian Federation
Konstantin A. Modestov — senior lecturer of the Department of General and Applied Physics; junior researcher at the International Scientific Center for Fundamental Research in the Field of Natural and Construction Sciences named after Honored Scientist of the Russian Federation Professor Yu.A. Rossikhin
26 Yaroslavskoe shosse, Moscow, 129337;
84, 20 let Oktyabrya st., Voronezh, 394006
RSCI AuthorID: 635355, Scopus: 57202800599, ResearcherID: C-9948-2016
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Review
For citations:
Saiyan S.G., Marasanova A.A., Ivanchenko K.D., Modestov K.A. Harmonic longitudinal waves in discretely inhomogeneous viscoelastic rods. Vestnik MGSU. 2026;21(2):207-218. (In Russ.) https://doi.org/10.22227/1997-0935.2026.2.207-218
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