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.

The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation / Kaplunov, Julius; Nobili, Andrea. - In: JOURNAL OF VIBRATION AND CONTROL. - ISSN 1077-5463. - STAMPA. - 23:12(2017), pp. 2014-2022. [10.1177/1077546315606838]

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

NOBILI, Andrea
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.
18-set-2015
23
12
2014
2022
The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation / Kaplunov, Julius; Nobili, Andrea. - In: JOURNAL OF VIBRATION AND CONTROL. - ISSN 1077-5463. - STAMPA. - 23:12(2017), pp. 2014-2022. [10.1177/1077546315606838]
Kaplunov, Julius; Nobili, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/1082868
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