Pole-residue method for dynamic response analysis of floating structures depending on decoupled Cummins equation

Abstract

This study proposes a new dynamic response estimation algorithm for floating structures based on the pole-residue method, which can be used to calculate the dynamic response induced by the wave force and the transient response created by initial conditions. The proposed algorithm deals with the Cummins equation in the Laplace domain, which can avoid the integral computation of the convolution items and the error accumulation problem in the process of numerical integration. One theoretical improvement is that the transfer function obtained by the Laplace transform is decoupled and the corresponding poles and residues are calculated. Consequently, the coupling system of the floating body and fluid is replaced with the calculated poles and residues, which greatly simplifies the procedure for dynamic response analysis. Furthermore, the method avoids the integral errors of the time-domain method and the application limits of the frequency-domain method, such as energy leakage, periodic hypothesis, and allowing only the stable response calculation. Three test cases were employed to evaluate the performance of the proposed algorithm. The first case is a single degree of freedom (SDOF) system in the form of the Cummins equation. The example shows the implementation procedure of the proposed algorithm in detail. The results demonstrate that the proposed algorithm is able to simulate the dynamic response of the SDOF system accurately, and that its calculation efficiency is better than that of the Newmark-β method. The second case is a spar-type floating offshore wind turbine. Studies show that the dynamic responses estimated by the proposed algorithm match well with those of the time-domain method both in the stable and transient response analysis, and that the proposed algorithm has a better calculation accuracy. The final case is a Floating Production Storage and Offloading unit (FPSO) model. The studies of the FPSO model indicate that the estimated dynamic response obtained applying the proposed algorithm agrees well with that of the WASIM codes of SESAM, which further proves the validity of the proposed algorithm.