Numerical and Experimental Analysis of Water Wave Scattering by Floating Elastic Plates

Abstract

The response of one or more floating compliant disks to a monochromatic linear water wave is investigated theoretically and experimentally, in a regime where scattering effects dominate. A model is constructed assuming the disks behave as thin elastic plates, moving freely in a fluid domain of finite depth and infinite extent in the horizontal directions. The response of a single disk is devised first, using a novel version of the eigenfunction matching method, that accommodates a realistic Archimedean draught. The solution to the multiple-disk problem is obtained using Graf’s addition formula.

A unique series of wave tank experiments is reported that replicates as closely as possible the conditions of the model. An optical remote sensing device provides accurate measurements for the disk deflection. Theoretical and experimental data are compared in terms of the natural modes of vibration of the disk. The modal amplitudes are analysed for three different disk thicknesses, over a frequency range relevant to the regime of interest. Additional tests with two disks provide data for different spacings and angles between the disks.

For tests involving a single disk, good agreement is obtained overall for the dominant modes, although discrepancies appear consistently in the results. The influence of components of the experimental setup are analysed theoretically by extension of the original model to explain or discard their effect on the motion of the disk. For tests with two disks, evidence that the disks influence each other’s motion is found and reasonable agreement is obtained with the theory.