A Dirac δ function based frequency-domain algorithm for the offshore structural vibration considering non-zero initial conditions

For the structural design under dynamic loads, it is commonly assumed that the structure is initially in a static state, and time-domain or frequency-domain methods are employed to estimate the dynamic response of the system. However, for offshore engineering structures, the persistent action of environmental loads means that in the dynamic analysis the nonzero initial conditions like elastic deformation or vibration velocity must be properly accounted for. Under such circumstances, the dynamic response obtained using conventional frequency-domain methods might exhibit significant errors. To solve this problem, A novel frequency-domain algorithm are proposed to address the problem of the structural dynamic response under non-zero initial conditions. The discrete Fourier transform of the Dirac δ function and its first derivative are analytically derived using the Fourier transform and the finite difference method, forming the foundation of the proposed approach. This algorithm overcomes the numerical divergence often encountered in traditional frequency-domain algorithms for dynamic response analysis. The robustness and accuracy of the proposed algorithm are well verified through two numerical experiments, including a single degree of freedom system and an offshore monopile wind turbine subjected to combined wind, wave, and seismic loads under non-zero initial conditions.