The effect of periodic surface pressure on a rectangular elastic plate floating on shallow water |
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| Affiliation: | 1. BCAM – Basque Center for Applied Mathematics, Alameda de Mazarredo, 14, E48009 Bilbao, Basque Country, Spain;2. Ikerbasque – Basque Foundation for Science, Alameda Urquijo, 36-5, Plaza Bizkaia, E48011 Bilbao, Basque Country, Spain;1. Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, India;2. Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology Kharagpur, 721302, India;1. Institut de Mécanique des Fluides de Toulouse, UMR-CNRS-INPT-UPS-N 5502, Allée du Prof. Camille Soula, 31400 Toulouse, France;2. Faculty of Engineering, DICCA, School of Engineering, University of Genova, 1 via Montallegro, 16145 Genova, Italy;3. Department of Mechanical and Aerospace Engineering, Monash University, Clayton Campus, Victoria 3800, Australia;4. Department of Mechanical and Aerospace Engineering, Division of Biological Engineering, Monash University, Clayton Campus, Victoria 3800, Australia |
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| Abstract: | The steady-state behaviour of a floating elastic plate of bounded dimensions acted upon by a localized external load is investigated using linear shallow water theory. In the case of a plate of arbitrary shape, the problem reduces to solving a system of boundary-value integral equations supplemented with differential relations for the free edge of the plate. Using a rectangular plate as the example, the effect of the frequency of the periodic actions and the positions at which they are applied on the amplitudes of the normal flexures of the plate and of the directional pattern of surface waves far from the plate is investigated. It is shown that waveguide properties occur for an elongated plate. |
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