The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation

Kaplunov

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.

• Acceptance Date: Aug 25, 2015
• Publication Date: Sep 18, 2015
• Journal: Journal of Vibration and Control
• Print ISSN: 1077-5463
• Publisher: SAGE Publications
• Pages: 2014-2022
• DOI: https://doi.org/10.1177/1077546315606838
• Keywords: edge wave, Kirchhoff plate, Pasternak foundation, moving load, dispersion
• Publisher URL: http://dx.doi.org/10.1177/1077546315606838