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This study proposes replacing the spring and dashpot elements in the conventional tuned mass damper (TMD) by shape memory alloy (SMA) wires to form an SMA-based TMD to control the seismic responses of wind turbine tower. An equivalent linearization method is adopted to optimize the initial stiffness of SMA-based TMD by minimizing the root mean square (RMS) displacement of the tower. To have an insight into the control performance of SMA-based TMDs, a three-dimensional (3D) finite element model of a typical wind turbine tower is developed in ABAQUS, and tower responses without and with SMA-based TMDs when subjected to simulated and recorded ground motions are systematically analysed. For comparison, seismic responses of the tower controlled by the linear TMDs are also simulated. Numerical results show that the SMA-based TMDs can substantially mitigate seismic responses of the tower with almost the same reduction ratios as the linear TMDs, while the strokes of the SMA-based TMDs are much smaller than those of the linear TMDs. This merit makes the proposed method more practical compared to the conventional TMD-based method since the space in the nacelle and tower is normally very limited.

Offshore wind turbines can be built larger and lighter than they used to be due to the application of new materials. These large and flexible structures are vulnerable to external vibration sources such as wind, sea wave and earthquake excitations. It is necessary to mitigate the dynamic responses of offshore wind turbines to ensure the safety of these structures. Extensive research works have been carried out to mitigate the vibrations of the tower and/or blades of offshore wind turbines. Almost all the previous studies on the offshore wind turbine tower vibration control propose installing the control device at the top of the tower, i.e. in the nacelle. This method is effective to suppress the fundamental vibration mode of the tower, in which the maximum displacement occurs at the top of the tower. This practice is reasonable when wind and/or sea wave loadings are of interest since the energies of these vibration sources are concentrated in the low frequency range, and normally only the fundamental vibration mode of the tower is excited. On the other hand, offshore wind turbines may locate in the seismic prone areas, earthquake loading can be another vibration source during their lifetimes. When offshore wind turbines are subjected to earthquake excitation, higher vibration modes might be also excited. These higher vibration modes can further contribute to the structural responses and in certain circumstances they may even dominate the structural responses. In this case, installing the control device only in the nacelle will not be effective and more control devices should be installed at certain locations along the tower. In other words, one single control device will not be effective to control the tower vibrations if both the fundamental and higher vibration modes are of interest. This paper proposes using multiple tuned mass dampers (MTMDs) to control vibrations from the fundamental and higher modes of offshore wind turbine tower under multiple hazards, i.e. under the combined wind, sea wave and earthquake excitations. The effectiveness of the proposed method is numerically investigated. It should be noted that only the vibration of the tower is of interest in the present study. The vibration control of the blades is out of the scope of this paper, which will be further investigated.

Tuned mass dampers (TMDs) are widely adopted to control the adverse vibrations of engineering structures. To further improve the effectiveness of TMD, inerter was introduced into TMD recently to form inerter-based TMD systems. Similar to TMD, inerter-based TMDs should be carefully designed (optimized) in order to get their best control performances. In the previous studies on using inerter-based devices for seismic induced vibration control, the external excitation was normally simplified as a white noise and the inherent structural damping was ignored. However, it is well known that seismic excitation cannot be simply assumed as a white noise and damping always exists in the structure. The parameters obtained by the previous optimization procedures thus do not necessarily result in the best performance of the device. In the present study, the equations of motion of a single-degree-of-freedom (SDOF) structure equipped with three types of inerter-based TMDs subjected to seismic excitation are firstly developed. Instead of using a white noise as input, the filtered Kanai-Tajimi spectrum, which is characterized by the site damping and frequency, is adopted to model seismic ground motion. Then the effects of site damping, site frequency and structural damping on the inerter-based TMDs are comprehensively investigated and formulas are proposed to estimate the optimal parameters. Lastly, the responses of a structure without control and controlled by an inerter-based TMD under simulated and recorded earthquake ground motions are analysed by using MATLAB/Simulink. Numerical results show that the optimal parameters of inerter-based TMDs are significantly dependent on the site frequency and structural damping, while the site damping has little influence. Moreover, the accuracy of the proposed formulas is validated, and the control effectiveness of the inerter-based TMD is confirmed.