Multimode long-wave approximation for a viscoelastic coating subject to antiplane shear Multimode long-wave approximation for a viscoelastic

A general asymptotic approach involving multimode long-wave approximations is illustrated by a 2D time-harmonic scalar problem for the dynamic antiplane shear of a viscoelastic coating. For the first time, a 1D equation of motion with the coefficients depending on frequency parameters is derived. Th...

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Bibliographic Details
Published inZeitschrift für angewandte Mathematik und Physik Vol. 75; no. 6
Main Authors Erbaş, Barış, Itskov, Mikhail, Kaplunov, Julius, Prikazchikov, Danila
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2024
Subjects
Engineering
Mathematical Methods in Physics
Theoretical and Applied Mechanics
Multimode
Long wave
74K20
74H10
Viscoelastic
Asymptotic
74BXX
Coating
74J05
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Summary:A general asymptotic approach involving multimode long-wave approximations is illustrated by a 2D time-harmonic scalar problem for the dynamic antiplane shear of a viscoelastic coating. For the first time, a 1D equation of motion with the coefficients depending on frequency parameters is derived. The associated dispersion relation also seems to be a fresh development approximating its exact counterpart near the vicinities of all the cut-off frequencies. As might be expected, the developed formulation is not valid for short wavelength patterns. At the same time, as it is shown for a δ -type loading, it proves to be robust for various scenarios dominated by long-wave response.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-024-02382-w