Plane waves and uniqueness theorems in the theory of viscoelastic mixtures

In the present paper, the linear theory of binary viscoelastic mixtures is considered. The basic properties of plane harmonic waves are established. Green’s first identity for 3D bounded and unbounded domains is obtained. On the basis of this identity the uniqueness theorems of regular (classical) s...

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Bibliographic Details
Published inActa mechanica Vol. 228; no. 5; pp. 1835 - 1849
Main Author Svanadze, Maia M.
Format Journal Article
LanguageEnglish
Published Vienna Springer Vienna 01.05.2017
Springer
Springer Nature B.V
Subjects
Boundary value problems
Classical and Continuum Physics
Control
Dynamical Systems
Engineering
Engineering Thermodynamics
Heat and Mass Transfer
Mathematical analysis
Original Paper
Plane waves
Planes
Solid Mechanics
Theorems
Theoretical and Applied Mechanics
Uniqueness theorems
Vibration
Viscoelasticity
74G30
74E30
74D05
74J05
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Summary:In the present paper, the linear theory of binary viscoelastic mixtures is considered. The basic properties of plane harmonic waves are established. Green’s first identity for 3D bounded and unbounded domains is obtained. On the basis of this identity the uniqueness theorems of regular (classical) solutions of the boundary value problems (BVPs) of steady vibrations are proved. Then these theorems are established in the quasi-static case. Finally, the uniqueness theorems for the first internal and external BVPs of steady vibrations in general and quasi-static cases are proved under weak condition on the viscoelastic constants.
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ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-017-1799-2