Rapid decoupling Laplace-domain algorithm for dynamic response estimation of offshore structures with asymmetric system matrices

Abstract

The vibrating differential equation of offshore structures with asymmetric system matrices cannot be decoupled using normal or complex modes. The dynamic response analysis of offshore structures is employed only using the frequency-domain method or step-by-step integration method, owing to which we cannot avoid the limitations of those methods, such as relying the on calculation time step, low calculation efficiency, and steady-state response analysis. To address these problems, a Laplace-domain algorithm based on the poles and corresponding residues of a decoupled vibrating system and exciting wave force is proposed to deal with the dynamic response analysis of offshore structures with asymmetric system matrices. A theoretical improvement is that the vibrating equation with asymmetric system matrices is decoupled by the lower parts of the left and right eigenvectors, providing the possibility of solving the vibrating equation based on the decoupled equations. Meanwhile, this method analyzes the dynamic response of offshore structures in the Laplace domain, indicating that the proposed method is insensitive to the calculation time step and has a higher calculation accuracy. Considering that this algorithm can calculate the transient response caused by the initial conditions, the wave force can be divided into a series of small segments, and the dynamic response is connected by the initial conditions of the small segments, thereby considerably improving the computing efficiency of the dynamic response analysis. Three test cases were applied to evaluate the performance of the proposed algorithm. The results show that (1) the proposed algorithm can estimate the dynamic response of offshore structures with asymmetric system matrices both in the process of transient and steady-state response analysis; (2) the computational accuracy of the proposed algorithm is insensitive to the calculation time step, which has a more stable calculation result compared with the Newmark-β method; and (3) the proposed algorithm has a higher calculational efficiency owning to the transient analysis capability.