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

Erbaş, Barış; Itskov, Mikhail; Kaplunov, Julius; Prikazchikov, Danila

Authors

Barış Erbaş

Mikhail Itskov



Abstract

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.

Citation

Erbaş, B., Itskov, M., Kaplunov, J., & Prikazchikov, D. (2024). Multimode long-wave approximation for a viscoelastic coating subject to antiplane shear. Zeitschrift für angewandte Mathematik und Physik, 75(6), Article 234. https://doi.org/10.1007/s00033-024-02382-w

Journal Article Type Article
Acceptance Date Nov 4, 2024
Online Publication Date Nov 27, 2024
Publication Date Dec 1, 2024
Deposit Date Dec 2, 2024
Publicly Available Date Dec 2, 2024
Journal Zeitschrift für angewandte Mathematik und Physik
Print ISSN 0044-2275
Publisher Birkhäuser Verlag
Peer Reviewed Peer Reviewed
Volume 75
Issue 6
Article Number 234
DOI https://doi.org/10.1007/s00033-024-02382-w
Keywords Asymptotic, 74K20, 74J05, 74H10, Long wave, Coating, Multimode, Viscoelastic, 74BXX
Public URL https://keele-repository.worktribe.com/output/984767
Publisher URL https://link.springer.com/article/10.1007/s00033-024-02382-w

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Multimode long-wave approximation for a viscoelastic coating subject to antiplane shear (381 Kb)
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Licence
https://creativecommons.org/licenses/by/4.0/

Publisher Licence URL
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Copyright Statement
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.






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