Response mitigation of offshore wind turbine towers using negative stiffness amplifying compliant liquid dampers-inerter exposed to wind waves and earthquakes

The efficacy of compliant liquid dampers-inerter (CLDI) has been proven to improve the dynamic response of monopile offshore wind turbine towers (MOWTT). The benefit of a negative stiffness element is investigated as this study proposes a new negative stiffness amplifying compliant liquid damper-inerter (NSA-CLDI). The prime novelty of the work lies in the detailed mathematical modelling of the MOWTT-NSA-CLDI combined system by forming the equations of motion and exploring the damper's efficiency in reducing MOWTT responses caused by wind, waves, and earthquakes. As an example, the 5-MW NREL MOWTT is chosen. Five separate wind speeds and 100 earthquake ground motion records are considered. As a result, the average values of the maximum structural displacement and acceleration are selected as objective functions (OFs): the root mean square (RMS) responses for wind-wave loadings and peak responses for earthquake loadings. The multi-objective Grey Wolf optimization is carried out by minimizing the four OFs in side-side (SS) and fore-aft (FA) directions, and two sets of optimum NSA-CLDI parameters are identified. The control efficacy of NSA-CLDI is scrutinized in the time and frequency domains and compared with CLDI using the determined optimal parameters in two vibrational directions of the MOWTT. The results reveal that NSA-CLDI's performance in effectively controlling the SS and FA vibrations is superior to CLDI.