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

Zeitschrift für angewandte Mathematik und Physik, vol. 75

Abstract

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.

Authors 4

1. Barış Erbaş corresponding

   Eskisehir Technical University

   Affiliation as printed

   Department of Mathematics, Eskisehir Technical University, Eskisehir, Turkey

   Department of Mathematics, Eskisehir Technical University, Yunus Emre Campus, 26470, Eskisehir, Turkey

2. Mikhail Itskov corresponding Aachen Department of Continuum Mechanics

   Keele University · RWTH Aachen University

   Affiliation as printed

   Department of Continuum Mechanics, RWTH Aachen University, Aachen, Germany

   School of Computer Science and Mathematics, Keele University, Keele, UK

   Department of Continuum Mechanics, RWTH Aachen University, 52062, Aachen, Germany

3. Julius Kaplunov corresponding Aachen Department of Continuum Mechanics

   Keele University · RWTH Aachen University

   Affiliation as printed

   Department of Continuum Mechanics, RWTH Aachen University, Aachen, Germany

   School of Computer Science and Mathematics, Keele University, Keele, UK

   Department of Continuum Mechanics, RWTH Aachen University, 52062, Aachen, Germany

4. Danila A. Prikazchikov corresponding

   Keele University

   Affiliation as printed

   School of Computer Science and Mathematics, Keele University, Keele, UK

   School of Computer Science and Mathematics, Keele University, Keele, ST5 5BG, UK