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The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kaplunov, J. Nobili, Andrea |
| Copyright Year | 2017 |
| 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. |
| Starting Page | 2014 |
| Ending Page | 2022 |
| Page Count | 9 |
| File Format | PDF HTM / HTML |
| DOI | 10.1177/1077546315606838 |
| Volume Number | 23 |
| Alternate Webpage(s) | http://eprints.keele.ac.uk/1511/1/KaplunovNobili15.pdf |
| Alternate Webpage(s) | https://iris.unimore.it/retrieve/handle/11380/1082868/155917/edgepast.pdf |
| Alternate Webpage(s) | https://doi.org/10.1177/1077546315606838 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
