Multiply heaving bodies in the time-domain: Symmetry and complex resonances

Abstract

The time-domain linear water wave problem for multiple bodies which are constrained to move in heave after being given an arbitrary initial displacement is considered. It is shown that the solution can be calculated in a simple and efficient method using the frequency domain solution. The resonant behaviour of the system is then investigated and an approximation to the solution using the singularity expansion method derived. A method to exploit any symmetry in the multiple body geometry, which makes the calculations more efficient and simplifies the analysis, is presented. Numerical calculations are performed for truncated cylinders, using bespoke code that computes the solution for complex frequencies. A method to approximate the solution for complex frequencies using results for real frequencies is derived and this is used to make calculations for heaving hemispheres using existing general purpose computer code.