A coupled damped harmonic oscillator model for arbitrary arrays of floating cylinders using homotopy methods

Abstract

A coupled damped harmonic oscillator model is derived for the long-time motion of an array of floating cylinders moving in heave, forced by a prescribed initial displacement. Eigenmodes of the coupled damped harmonic oscillator model are set to be the complex resonances of the corresponding linear potential theory model of the array. Thus, the solution of the coupled damped harmonic oscillator model has the same form as the singularity expansion method. The derivation of the coupled damped harmonic oscillator model is underpinned by a homotopy method to calculate the complex resonances for arbitrary arrays. A recursive homotopy method is used to study the complex resonances as one of the geometrical parameters is varied. The coupled damped harmonic oscillator model is shown to give accurate approximations of the full linear solutions, except for exceptional cases in which additional complex resonances appear.