A low-frequency multimode approximation for a thin elastic sandwich

European Journal of Mechanics - A/Solids, vol. 121, pp. 106309

Abstract

Antisymmetric low-frequency motion of a three-layered plate is considered within the framework of 3D elasticity. The skin (outer) layers are assumed to be much stiffer than the core (inner) one. The leading order 2D multimode approximation is derived. It incorporates three asymptotic behaviours, governed by bending and shear scalings as well as by a specific one related to the transition from bending to shear regimes. Dispersion of time-harmonic and evanescent waves is investigated over the frequency band involving the smallest cut-off. It is shown that the obtained polynomial expansions coincide with the long-wave low-frequency approximations of the transcendental dispersion relations arising in plane and antiplane elasticity.

Authors 3

1. Barış Erbaş

   Keele University · Eskisehir Technical University

   Affiliation as printed

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

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

2. Ludmila A. Prikazchikova corresponding

   Keele University

   Affiliation as printed

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

3. Julius Kaplunov Aachen Department of Continuum Mechanics

   RWTH Aachen University · Keele University

   Affiliation as printed

   Department of Continuum Mechanics, RWTH Aachen University, Kackertstraße 9, 52072, Aachen, Germany

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