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

• Published in: Zeitschrift für angewandte Mathematik und Physik Vol. 75; no. 6
• Main Authors: Erbaş, Barış, Itskov, Mikhail, Kaplunov, Julius, Prikazchikov, Danila
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.12.2024
• Subjects: Approximation; Equations of motion; Viscoelasticity
• ISSN: 0044-2275; 1420-9039
• DOI: 10.1007/s00033-024-02382-w

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.