A dynamic response analysis method with high-order accuracy for fixed offshore structures based on a normalised expression of external loadings

Abstract

A new step-by-step dynamic response analysis method is proposed for fixed offshore structures in the time domain with high-order accuracy. The basic principle of the proposed method is to normalise an arbitrary loading into the form of complex exponents with arbitrary-order derivatives, permitting the high-order Taylor expansion of dynamic response components (acceleration, velocity, and displacement) in theory. The proposed method is more accurate than other proposed methods, especially for structures subjected to short-term, high-energy loading with data collected using a limited sampling frequency. The response obtained has higher-order accuracy than that obtained with the widely used Newmark-β method, which only has second-order accuracy because of the assumption of acceleration linearisation. Four examples are used to demonstrate the correctness and accuracy of the proposed method. The first numerical example uses a single-degree-of-freedom (SDOF) system to demonstrate the calculated results obtained using different orders of Taylor expansion with the proposed method. The comparison with the analytical result and the result obtained with the Newmark-β method shows that the proposed method is less sensitive to the sampling frequency and that even the accuracy of the third-order Taylor expansion-based method is higher than that of the Newmark-β method. In the second example, the third-order Taylor expansion-based method is used to calculate the dynamic response of a three-degree-of-freedom (3DOF) system under earthquake excitation sampled at a fixed frequency to show that the proposed method can determine the structural dynamic response under an arbitrary form of loading better accuracy than the Newmark-β method. In the third example, a numerical monopile offshore wind turbine (OWT) is used for verifying the feasibility of the proposed method in calculating the dynamic response of fixed offshore structures. Finally, measurements of a cantilever beam with similar properties of monopile OWT under harmonic excitations and random excitations are used to demonstrate the proposed method and illustrate its potential values for application to dynamic response analysis of fixed offshore structures.