We develop a mathematical model of a large-scale cracked horizontal axis wind turbine (HAWT) describing the flapping flexure of the flexible tower and blades. The proposed model has enough fidelity to be used in health monitoring applications. The equations of motion account for the effect of the applied aerodynamic forces, modeled using the blade element momentum (BEM) theory, and the location and shape of a crack introduced into one of the blades. We first examine the static response of the HAWT in presence of the crack, and then we formulate the eigenvalue problem and determine the natural frequencies and associated mode shapes. We show that both shape and location of the crack influence the first four natural frequencies. The dynamic response of the HAWT subjected to wind and gravity is obtained using a Galerkin procedure. We conduct a parametric analysis to investigate the influence of the crack on the eigenstructure and overall dynamics. The simulations depict that the first four natural frequencies are reduced as the crack size become more important. We also conclude that the tower root moment may be considered as potential indicators for health monitoring purposes.

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