A lagrangian alternating frequency-time method for the calculation of the harmonic response of 3D structures in contact with friction is presented. Following the ideas of Nacivet et al. [1], the set of nonlinear equations is solved in the frequency domain while the unilateral contact and friction laws are checked in the time domain. A large number of contact elements with both normal and tangential degrees of freedom can be taken into account. This procedure is used to study a 3D model of a turbomachinery blade with dovetail attachment. A component mode synthesis is carried out and an exact dynamic reduction is then performed in the frequency domain. Only the relative displacements of the node-to-node 3D contact elements are kept in the final set of non linear equations. The blade and the corresponding jaw are subject to a constant centrifugal force and a harmonic force. The nonlinear frequency response, the normal pressure distribution and the localization of the energy dissipation are presented and discussed.