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The present paper proposes a novel two-dimensional non-linear tuned massdamper inerter (2d-NTMDI) to effectively mitigate bi-directional structuralresponses. The 2d-NTMDI consists of a mass and two sets of springs, dashpotsand inerters configured in two axes. The resultant restoring forces arenonlinear with respect to the displacements in two axes. While the proposednovel 2d-NTMDI has the capability of mitigating bi-directional vibrationssimultaneously, the system nonlinearity complicates the optimization. Anumerical search method is adopted to determine the optimum design parametersof the 2d-NTMDI. To evaluate the effectiveness, the proposed 2d-NTMDI isdeployed in a 5MW-wind turbine blade suffering from bi-directional vibrationsin the edgewise and flapwise directions. To this end, an analytical model of awind turbine blade with a 2d-NTMDI is established. The wind loading is computedusing blade element momentum theory. The effectiveness of the 2d-NTMDI isexamined under different loading conditions. Also, the fatigue damage of thewind turbine blades is calculated according to the rain-flow cycle countingapproach and Miner's law. It is concluded that the optimized design 2d-NTMDIcan prolong the blade fatigue life by $35\%$.

A novel two dimensional nonlinear tuned mass damper inerter and its application in vibration mitigation of wind turbine blade