A new residue-based dynamic analysis method for offshore structures with non-zero initial conditions
Different from the traditional time-domain methods, which usually employ a step-by-step procedure for response estimation of structures with non-zero initial conditions, a new time-domain response estimation method is proposed by using separated residues corresponding to original external loadings and non-zero initial conditions, to provide a more efficient algorithm for offshore structures with non-zero initial conditions. The key of the proposed method is that responses of the system are divided into three contributions in the Laplace domain: the first comes from the original external loadings, the second from the initial displacements, and the last from a simultaneous combination of initial displacements and velocities. One theoretical development of the proposed method is that these three parts are all represented by separated residues that can be estimated by using the state-space model, which is also the actual reason why each part of the Laplace-domain responses of the system can be easily transformed back to the time domain in terms of the inverse Laplace transform. Compared with the traditional time-domain methods, responses from the proposed method are directly estimated by utilizing the inverse Laplace transform, which implies that estimated time-domain responses will be continuous in the time domain, so more accurate results can be expected. In addition, the proposed method avoids the procedure of a step-by-step estimation; therefore, better computational efficiency can also be predicted. Three numerical examples and one experiment are used to investigate the performance of the proposed method: the first is a single-degree-of-freedom (SDOF) system to illustrate the procedure, the second is a six-DOF system aiming at extending the proposed method to multiple-DOF (MDOF) systems, and the last is a typically studied engineering structure, i.e., a beam model, to show the potential engineering applications of the proposed method. Numerical results show that the proposed method not only can provide much more accurate time-domain responses compared with those from the traditional time-domain methods, even when the time step used is not so accurate, but also has better computational efficiency, e.g., in the third example, the traditional time-domain method takes 172.39 s during the estimation of responses with 10 s, while the proposed method takes only 13.01 s. Finally, an experimental fixed offshore platform conducted at the lab of Ocean University of China is used to demonstrate the proposed method.