Frequency response estimation of floating structures by representation of retardation functions with complex exponentials

This article aims at proposing a new frequency-domain response estimation method for floating structures by dealing with fluid memory effects from the view point of signal decomposition. One development is that the convolution terms are decomposed and replaced by a series of poles and corresponding residues in the Laplace domain, based on the estimated added mass and damping matrices of the structure. The advantage of the proposed method is that the frequency-dependent motion equations in the time domain can then be transformed to the Laplace domain without requiring Laplace-domain expressions of the added mass and damping. The second is that exciting wave forces are not limited to harmonic components, and each component can be purely harmonic, damped harmonic or purely damped exponential. Therefore, the problem of frequency leakage caused by using the Fourier transform can be avoided, which also means estimations of frequency-domain responses can be improved accordingly. Four examples are used to investigate the performance of the proposed method. The first is a simple retardation function, which is based on a purely analytical relationship, and it satisfies all the properties of the convolution terms in the time and frequency domains simultaneously, demonstrating the correctness of using the complex exponentials to represent the retardation functions. The second is a single degree of freedom (SDOF) mathematical model subjected to a synthesized exciting wave force. The numerical results show that the frequency response function (FRF) estimated using this approach matches well with that of the traditional method. For exciting wave forces, the proposed method can yield a better frequency-domain estimation because the proposed method is not limited to a frequency resolution. To extend the proposed method to multiple DOF systems and address applications to marine structures, a semi-submersible (SEMI) and a FPSO model in SESAM is employed respectively. One can draw the following conclusions from the numerical results: (1) the FRFs of the floating structures can be obtained by replacing the convolution terms with a series of poles and corresponding residues in the Laplace domain, and they match well with those from the traditional method; and (2) the new method can provide almost identical response estimates as those of the traditional frequency-domain method when the exciting wave forces are truly composed of purely harmonic components.