Multimode long-wave approximation for a viscoelastic coating subject to antiplane shear
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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| Published in | Zeitschrift für angewandte Mathematik und Physik Vol. 75; no. 6 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Heidelberg
Springer Nature B.V
01.12.2024
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| 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
$$\delta $$
δ
-type loading, it proves to be robust for various scenarios dominated by long-wave response. |
|---|---|
| AbstractList | 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
$$\delta $$
δ
-type loading, it proves to be robust for various scenarios dominated by long-wave response. 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. |
| ArticleNumber | 234 |
| Author | Erbaş, Barış Itskov, Mikhail Kaplunov, Julius Prikazchikov, Danila |
| Author_xml | – sequence: 1 givenname: Barış orcidid: 0000-0003-3211-9930 surname: Erbaş fullname: Erbaş, Barış – sequence: 2 givenname: Mikhail surname: Itskov fullname: Itskov, Mikhail – sequence: 3 givenname: Julius surname: Kaplunov fullname: Kaplunov, Julius – sequence: 4 givenname: Danila orcidid: 0000-0001-7682-3079 surname: Prikazchikov fullname: Prikazchikov, Danila |
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| Title | Multimode long-wave approximation for a viscoelastic coating subject to antiplane shear |
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