<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The paper deals with free and forced vibrations of a horizontal thin elastic plate submerged in an infinite layer of fluid of constant depth. In free vibrations, the pressure load on the plate results from assumed displacements of the plate. In forced vibrations, the fluid pressure is mainly induced by water waves arriving at the plate. In both cases, we have a coupled problem of hydrodynamics in which the plate and fluid motions are coupled through boundary conditions at the plate surface. At the same time, the pressure load on the plate depends on the gap between the plate and the fluid bottom. The motion of the plate is accompanied by the fluid motion. This leads to the so-called co-vibrating mass of fluid, which strongly changes the eigenfrequencies of the plate. In formulation of this problem, a linear theory of small deflections of the plate is employed. In order to calculate the fluid pressure, a solution of Laplace’s equation is constructed in the doubly connected infinite fluid domain. To this end, this infinite domain is divided into sub-domains of simple geometry, and the solution of the problem equation is constructed separately for each of these domains. Numerical experiments are conducted to illustrate the formulation developed in this paper.</p></abstract>

The paper deals with free and forced vibrations of a horizontal thin elastic plate submerged in an infinite layer of fluid of constant depth. In free vibrations, the pressure load on the plate results from assumed displacements of the plate. In forced vibrations, the fluid pressure is mainly induced by water waves arriving at the plate. In both cases, we have a coupled problem of hydrodynamics in which the plate and fluid motions are coupled through boundary conditions at the plate surface. At the same time, the pressure load on the plate depends on the gap between the plate and the fluid bottom. The motion of the plate is accompanied by the fluid motion. This leads to the so-called co-vibrating mass of fluid, which strongly changes the eigenfrequencies of the plate. In formulation of this problem, a linear theory of small deflections of the plate is employed. In order to calculate the fluid pressure, a solution of Laplace’s equation is constructed in the doubly connected infinite fluid domain. To this end, this infinite domain is divided into sub-domains of simple geometry, and the solution of the problem equation is constructed separately for each of these domains. Numerical experiments are conducted to illustrate the formulation developed in this paper.

Vibrations of a Horizontal Elastic Band Plate Submerged in Fluid of Constant Depth

Institute of Hydro-Engineering, Polish Academy of Sciences, ul. Kościerska 7, 80-328 Gdańsk,

Archives of Hydro-Engineering and Environmental Mechanics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The paper deals with free and forced vibrations of a horizontal thin elastic plate submerged in an infinite layer of fluid of constant depth. In free...

Vibrations of a Horizontal Elastic Band Plate Submerged in Fluid of Constant Depth

Published Online: Apr 04, 2017

Page range: 191 - 213

Received: Oct 26, 2016

DOI: https://doi.org/10.1515/heem-2016-0012

Keywords
elastic plate, free vibrations, forced vibrations, eigenfrequencies, co-vibrating mass of fluid

© 2016 Kazimierz Szmidt et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Vibrations of a Horizontal Elastic Band Plate Submerged in Fluid of Constant Depth

Published Online: Apr 04, 2017

Page range: 191 - 213

Received: Oct 26, 2016

DOI: https://doi.org/10.1515/heem-2016-0012

Keywordselastic plate, free vibrations, forced vibrations, eigenfrequencies, co-vibrating mass of fluid

© 2016 Kazimierz Szmidt et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
elastic plate, free vibrations, forced vibrations, eigenfrequencies, co-vibrating mass of fluid