<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The paper deals with forced vibrations of a horizontal thin elastic plate submerged in a semi-infinite layer of fluid of constant depth. The pressure load on this plate is induced by water waves arriving at the plate. This load is accompanied by pressure resulting from the motion of the plate. The plate and fluid motions depend on boundary conditions, and, in particular, the pressure load depends on the width of the gap between the plate and the bottom. In theoretical description of the phenomenon, we deal with a coupled problem of hydrodynamics in which the plate and fluid motions are coupled through boundary conditions at the plate surfaces. The main attention is focused on transient solutions of the problem, which correspond to fluid (and plate) motion starting from rest. 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 a doubly connected fluid domain. With respect to the initial value problem considered, we confine our attention to a finite fluid domain. For a finite elapse of time, measured from the starting point, the solution in the finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. Because of the complicated structure of boundary conditions of the coupled problem considered, the fluid domain is divided into sub-domains of simple geometry, and the solutions of the problem equations are constructed separately in each of these domains. Numerical experiments have been conducted to illustrate the formulation developed in this paper.</p></abstract>

The paper deals with forced vibrations of a horizontal thin elastic plate submerged in a semi-infinite layer of fluid of constant depth. The pressure load on this plate is induced by water waves arriving at the plate. This load is accompanied by pressure resulting from the motion of the plate. The plate and fluid motions depend on boundary conditions, and, in particular, the pressure load depends on the width of the gap between the plate and the bottom. In theoretical description of the phenomenon, we deal with a coupled problem of hydrodynamics in which the plate and fluid motions are coupled through boundary conditions at the plate surfaces. The main attention is focused on transient solutions of the problem, which correspond to fluid (and plate) motion starting from rest. 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 a doubly connected fluid domain. With respect to the initial value problem considered, we confine our attention to a finite fluid domain. For a finite elapse of time, measured from the starting point, the solution in the finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. Because of the complicated structure of boundary conditions of the coupled problem considered, the fluid domain is divided into sub-domains of simple geometry, and the solutions of the problem equations are constructed separately in each of these domains. Numerical experiments have been conducted to illustrate the formulation developed in this paper.

Flow-induced Vibrations of a Horizontal Elastic Band Plate Submerged in Fluid of Finite Depth

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 forced vibrations of a horizontal thin elastic plate submerged in a semi-infinite layer of fluid of constant depth. The pressure load on...

Flow-induced Vibrations of a Horizontal Elastic Band Plate Submerged in Fluid of Finite Depth

Published Online: Aug 10, 2020

Page range: 101 - 130

Received: Dec 10, 2019

Accepted: Feb 28, 2020

DOI: https://doi.org/10.1515/heem-2019-0007

Keywords
elastic plate vibrations, surface waves, initial value problem, coupled problem

© 2019 Kazimierz Szmidt et al., published by Sciendo

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

Flow-induced Vibrations of a Horizontal Elastic Band Plate Submerged in Fluid of Finite Depth

Published Online: Aug 10, 2020

Page range: 101 - 130

Received: Dec 10, 2019

Accepted: Feb 28, 2020

DOI: https://doi.org/10.1515/heem-2019-0007

Keywordselastic plate vibrations, surface waves, initial value problem, coupled problem

© 2019 Kazimierz Szmidt et al., published by Sciendo

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

Keywords
elastic plate vibrations, surface waves, initial value problem, coupled problem