A rapid response calculation method for symmetrical floating structures based on state–space model solving in hybrid time-Laplace domain

Abstract

The article focuses on proposing a new hybrid time-Laplace domain response calculation method for symmetrical floating structures by solving Cummins equation, which is depending on the state–space model identified from transfer function. Different from a time or frequency domain method, the proposed approach estimates the state–space model of a floating structure system from the transfer function in the Laplace domain and calculates the response by considering the exciting forces as an input of the state–space model. Implementing complex exponential decomposition to the retardation functions, the retardation functions in the Laplace domain are expressed using a series of poles and the corresponding residues, which avoids the numerical integral of the convolution terms in the Cummins equation and greatly improves the computational efficiency during the process of a dynamic response analysis. Three examples are applied to investigate the validity of the proposed method. The first is a simple single degree of freedom mathematical model excited by an irregular wave. Studies have shown that the response calculated by the proposed method matches well with that of a traditional Newmark-β method. Meanwhile, this approach is insensitive to the interval time of the calculation and consumes less calculation time, which means that the proposed method has higher precision and computational efficiency. The last two examples are a spar-type offshore wind turbine and a semi-submersible platform model (SEMI) in SESAM, which extend the proposed method to solve the response estimation problem of marine structures. The results of the spar-type floating structure show that the estimated responses when using the proposed method are in good agreement with the results of the traditional time domain method. By studying the response calculation of SEMI, the following conclusions can be obtained: (1) the estimated responses match well with the traditional time domain method and WASIM code of SESAM, and (2) the calculation time of the new approach is reduced significantly compared with the Newmark-β method especially under a long simulation time.