This work concerns the vibration damping in the low frequency range of woven composite fan blades of a turbojet engine. The interest is to increase lifespan and avoid flutter phenomena by reducing the vibration amplitude. The solution considered in this work consists in using piezoelectric elements integrated into the composite structure and connected to a passive electric circuit usually called shunt. The first part of this work will focus on the development of a predictive finite element model of the structure coupled to the piezoelectric elements to quantify the performance of the damping device. Comparisons between simulations and experiments will be also presented. It will be shown that purely passive resonant shunts can significantly reduce the level of vibration of the first bending modes of a complex industrial structure. The importance of placement and geometry of the piezoelectric elements in order to maximize the electrotechnical coupling, and thus the efficiency of the system, will be also highlighted.