Kaplunov, J and Nobili, A (2015) The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation. Journal of Vibration and Control, 23 (12). pp. 2014-2022.

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Abstract

In this paper, the bending waves propagating along the edge of a semi-infinite Kirchhoff plate resting on a two-parameter Pasternak elastic foundation are studied. Two geometries of the foundation are considered: either it is infinite or it is semi-infinite with the edges of the plate and of the foundation coinciding. Dispersion relations along with phase and group velocity expressions are obtained. It is shown that the semi-infinite foundation setup exhibits a cut-off frequency which is the same as for a Winkler foundation. The phase velocity possesses a minimum which corresponds to the critical velocity of a moving load. The infinite foundation exhibits a cut-off frequency which depends on its relative stiffness and occurs at a nonzero wavenumber, which is in fact hardly observed in elastodynamics. As a result, the associated phase velocity minimum is admissible only up to a limiting value of the stiffness. In the case of a foundation with small stiffness, asymptotic expansions are derived and beam-like one-dimensional equivalent models are deduced accordingly. It is demonstrated that for the infinite foundation the related nonclassical beam-like model comprises a pseudo-differential operator.

Item Type: Article
Uncontrolled Keywords: edge wave, Kirchhoff plate, Pasternak foundation, moving load, dispersion
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Depositing User: Symplectic
Date Deposited: 14 Mar 2016 10:36
Last Modified: 24 Apr 2019 08:23
URI: http://eprints.keele.ac.uk/id/eprint/1511

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