Abstract
The motion of a circular elastic plate floating on the surface is investigated in the time-domain. The solution is found from the single frequency solutions, and the method to solve for the circular plate is given using the eigenfunction matching method. Simple plane incident waves with a Gaussian profile in wavenumber space are considered, and a more complex focused wave group is considered. Results are given for a range of plate and incident wave parameters. Code is provided to show how to simulate the complex motion.
Highlights
The single frequency solution for the linear water wave problem is extensively used to model the hydroelastic response of very large floating structures, container ships, or an ice floe [1,2,3,4]
The solution for incident waves in two-dimensions was given in finite depth by [25,26,27] and in shallow water in two by [21,22] and three–dimensions by [23]
Even for the case of high amplitude waves, the linear wave problem remains valid for a floating plate [39], and this model continues to the basis of offshore engineering and scattering by an ice floe
Summary
The single frequency solution for the linear water wave problem is extensively used to model the hydroelastic response of very large floating structures, container ships, or an ice floe [1,2,3,4]. The solution for incident waves in two-dimensions was given in finite depth by [25,26,27] and in shallow water in two by [21,22] and three–dimensions by [23]. The eigenfunction matching method has been applied to many floating elastic plate problems. The solution method was first described in [7] and this is where the solution of the special dispersion equation for a floating elastic plate was introduced. We present here a solution to the time-dependent problem of a floating circular plate subject to incident wave forcing. The present work aims to show how the time-domain solution can be found straightforwardly from the frequency domain solution. We note that the code which accompanies this work is an essential part of it, and this has not been made available previously
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