Anti-plane waves in an elastic thin strip with surface energy

Mikhasev, G. I.;Botogova, M. G.;Eremeyev, V. A.

2022-01-01

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Abstract

We consider anti-plane motions of an elastic plate taking into account surface energy within the linear Gurtin–Murdoch surface elasticity. Two boundary-value problems are considered that describe complete shear dynamics of a plate with free faces or with free and clamped faces, respectively. These problems correspond to anti-plane dynamics of an elastic film perfectly or non-perfectly attached to a rigid substrate. Detailed analysis of dispersion relations is provided. In particular, the influence of the ratio of a plate thickness to characteristic length on the dispersion curves is analysed.