Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Wilde M. V., Sergeeva N. V. Development of Asymptotic Methods for the Analysis of Dispersion Relations for a Viscoelastic Solid Cylinder. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2017, vol. 17, iss. 2, pp. 183-195. DOI: 10.18500/1816-9791-2017-17-2-183-195, EDN: ZEVXBF

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
22.05.2017
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Language: 
Russian
Heading: 
Mechanics
UDC: 
539.3
DOI: 
10.18500/1816-9791-2017-17-2-183-195
EDN: 
ZEVXBF

Development of Asymptotic Methods for the Analysis of Dispersion Relations for a Viscoelastic Solid Cylinder

Autors: 
Wilde Maria Vladimirovna, Saratov State University
Sergeeva Nadezhda Viktorovna, Saratov State University
Abstract: 

Propagation of time-harmonic waves in a viscoelastic solid cylinder is considered. Vibrations of the cylinder are described by three-dimensional viscoelasticity equations in  cylindrical coordinates. The stress-free surface boundary conditions are imposed. Viscoelastic properties are described by integral operators with a fractional-exponential kernel. For the case of a rational singularity parameter the method of asymptotic analysis of dispersion relations is proposed, which is based on the generalized power series expansion. For the axisymmetric waves the asymptotic expansions of the dispersion equation roots are obtained for low and high frequencies. The numerical results are presented to confirm the applicability of the proposed method.

Key words: 
dispersion equation
solid cylinder
viscoelasticity
asymptotics
singularity parameter
fractional parameter
fractional exponential function
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Received: 
15.01.2017
Accepted: 
28.04.2017
Published: 
31.05.2017
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