A rapid time-continuous response analysis algorithm for offshore structures by combination of modal superposition and complex exponential decomposition

Abstract

Dynamic response analysis for offshore structures plays an important role in the design stage to evaluate the performance of the designed structures. This study proposes a novel time-continuous dynamic response analysis algorithm for offshore structures, which is implemented in the Laplace domain depending on the decoupled vibrating differential equation and the complex exponential decomposition of external excitation. One theoretical development is that time-continuous dynamic response can be obtained according to discrete external excitation. The other is that the initial conditions can be considered in the process, thereby compensating for the weakness of the traditional frequency method. Concurrently, the computational efficiency of the proposed method is good benefitting from initial conditions considerable, and the algorithm is insensitive to the time step of the calculation compared with the time domain method. To monitor the performance of the algorithm, two numerical models and a physical model experiment are adopted. The first example is a simple numerical model of a cantilever beam, describing the entire process of the proposed method. The results indicate that the dynamic response of the vibrating system calculated by employing the proposed method is in good agreement with that obtained by the Newmark-β method. In addition, the algorithm yields an accurate dynamic response using a longer time step in the calculation, realizing better stability than the traditional Newmark-β method. The second example is a numerical model of a jacket offshore platform located at Liaodong Bay, Bohai Sea, which extends the algorithm to dynamic response analysis of offshore structures. The results of the studies show that the displacement response of the offshore structure calculated by the proposed method matches well with that yielded by the Newmark-β method under random initial conditions and exciting loads on the structure. It is found that the computational efficiency of the proposed algorithm is better than that of the time domain method. Finally, a physical cantilever model is applied to verify the correctness of the proposed method.