Complex resonances and the approximation of wave forcing for floating elastic bodies

The problem of a floating elastic body subject to linear wave forcing is considered. It is shown how the response curve can be approximated using complex resonances, or scattering frequencies as they are also known. A method is also derived to calculate approximately the position of the resonances using the solution for real frequencies only. The theory developed is applied to two problems, a two-dimensional floating elastic plate and a finite element–boundary element model for a container ship. For the floating elastic plate, the position of the resonances can be calculated exactly, and the exact solution is used to analyse the approximate solution. For the container ship, it is shown how the approximate theory can explain the solutions calculated for real frequencies by commercial software. It is shown that the sharp peaks in the response are characterized by a fixed shape in the frequency domain whose amplitude is determined by the incident forcing.

► We show that the response for hydroelastic bodies in the frequency domain can be approximated by a simple expansion based on the complex resonances.
► We also show that the response shape and frequency of peak is independent of forcing which only determines the amplitude.
► We also show how to calculate an approximation for the positions of the resonances using the solution for real frequencies only.
► We apply our theory to a floating elastic plate in two dimensions and to a container ship model.