Computing free motion of floating structures by pole-residue operations

Abstract Computing the free motion of a floating structure has often been conducted in the time domain by using the Cummins equation, which needs to perform a convolution integral at each time step and thus is costly in computational time. Assuming the frequency-domain solutions have been obtained from running a hydrodynamic package, the so-called Fourier transform method implements the computation in the frequency domain. Although this method can avoid time-stepping issues, it still needs to perform a complicated integration with respect to frequency at each time step. This study develops a novel pole-residue approach, which is more efficient than other existing methods, carried out in either the Laplace domain or the frequency domain. The key of the proposed approach is how to obtain the poles and residues of the system transfer function of a floating structure, as well as those of the free motion response. Knowing the poles and residues of the response allows it to be expressed immediately in the time domain. Three numerical examples are presented to illustrate the procedure and to verify the accuracy of the proposed method by comparing the motion responses obtained from the proposed method to those obtained from a time-domain method.