Vertical motion of a periodically driven floating disc

TL;DR

This study combines theory and experiments to analyze the vertical oscillations of floating discs under periodic forcing, providing insights into their dynamics and validating predictions with experimental data.

Contribution

It introduces a numerical method for solving the wavefield problem and compares theoretical predictions with experimental results for floating disc oscillations.

Findings

Excellent agreement between theory and experiments on oscillation amplitude

Computed added mass, wave damping, and spring coefficients across frequencies

Analytical results derived in the low-frequency limit

Abstract

We present the results of a combined theoretical and experimental investigation into the vertical dynamics of floating discs subjected to an imposed time-periodic forcing. The axisymmetric and inviscid wavefield is governed by a linear elliptic boundary value problem with mixed boundary conditions, wherein the no-penetration boundary condition is satisfied under the disc while the free surface boundary conditions are enforced away from it. The problem is solved by recasting the system of partial differential equations as a second-kind Fredholm integral equation which is then solved numerically. The solution furnishes a prediction for the dependence of the disc's oscillation amplitude on the forcing frequency, which exhibits excellent agreement with experiments. We interpret our results physically by computing the added mass, wave damping and effective spring coefficients of the disc, both numerically for a range of forcing frequencies and analytically in the low-frequency limit.