Nonlinear frequency-domain analysis of fixed structures subjected to morison-type wave forces

Abstract

For fixed offshore structures, a cumulant spectral analysis approach that is based on correlation-functions of wave kinematics and Fourier transforms is proposed for evaluating variance, skewness and kurtosis of the nonlinear wave loadings and induced structural responses. The linear wave theory is adopted and the joint-Gaussianity of wave kinematics is assumed. To account for the super-harmonic phenomena and to facilitate frequency-domain analysis, nonlinear drag forces are approximated by higher-order polynomials. The methods of least squares and moment-based approximation are compared. For power spectral and trispetcral analyses of a LTI system driven by the local Morison force or modal wave force, the detailed procedures are presented. The proposed approach is found to be more numerically efficient than the traditional Volterra series based frequency-domain method and time-domain simulations. A good agreement of the numerical results obtained in the frequency and time domains is also observed.