  The present paper proposes a novel two-dimensional non-linear tuned mass
damper inerter (2d-NTMDI) to effectively mitigate bi-directional structural
responses. The 2d-NTMDI consists of a mass and two sets of springs, dashpots
and inerters configured in two axes. The resultant restoring forces are
nonlinear with respect to the displacements in two axes. While the proposed
novel 2d-NTMDI has the capability of mitigating bi-directional vibrations
simultaneously, the system nonlinearity complicates the optimization. A
numerical search method is adopted to determine the optimum design parameters
of the 2d-NTMDI. To evaluate the effectiveness, the proposed 2d-NTMDI is
deployed in a 5MW-wind turbine blade suffering from bi-directional vibrations
in the edgewise and flapwise directions. To this end, an analytical model of a
wind turbine blade with a 2d-NTMDI is established. The wind loading is computed
using blade element momentum theory. The effectiveness of the 2d-NTMDI is
examined under different loading conditions. Also, the fatigue damage of the
wind turbine blades is calculated according to the rain-flow cycle counting
approach and Miner's law. It is concluded that the optimized design 2d-NTMDI
can prolong the blade fatigue life by $35\%$.
