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The unwanted vibrations of offshore structures induced by wave or earthquake loads can lead to the reduction of the service life and fatigue failure of the offshore platforms. This paper introduces tuned inerter damper (TID) to a jacket offshore platform as passive control device for mitigating the excessive vibrations of platform structure induced by wave and earthquake loads. An analytical design method is proposed for jacket platforms and the influence of installation location on the modal response is investigated. The proposed design method can determine the optimal installation position and obtain the optimal design parameters by transform the original multi-degree of freedom (MDOF) system to a single DOF (SDOF) modal system. Two sets of closed-form solutions of which corresponding to wave and earthquake excitations are derived based on the    $${\mathrm{H}}_{2}$$  H 2 optimization criterion. Further, a practical 90 (m) high and 80 (m) deep in-water jacket offshore platform is used in numerical simulation and the wave forces are modeled using Morison’s equation. The case study finds that the optimal installation location of TID is deck level for both wave and earthquake loads. The proposed design method is validated by the numerical example and the results demonstrate that TID system can effectively mitigate the maximum, minimum, and RMS responses of jacket platforms. Besides, the TID is more effective when the jacket platform is under the action of waves and the tuning of TID according to earthquake load is more reliable when the jacket platform subjected to both wave and seismic loads.

Mitigating jacket offshore platform vibration under earthquake and ocean waves utilizing tuned inerter damper