The focus of this investigation is on the application of the quadratic manifold method for model order reduction of a geometrically nonlinear vibrating structure with friction contact. Quadratic mapping has recently shown its ability to accurately capture the vibrations of a slender structure with geometric nonlinearity [1]. The Component Mode Synthesis method is also a well-established reduction approach for structures with local nonlinearity [2]. In this method, the reduced vector of unknowns includes the contact degrees of freedom that leads to the addition of the corresponding static modes to the reduction space. In this study, the quadratic manifold method is employed while the static modes and their derivatives are considered. So the manifold is tangent to a subspace spanned by linear vibration modes and static modes and the manifold curvature is defined by their derivatives. The inclusion of the static modes better represents the behavior of a structure under nonlinear friction forces. The performance of this reduction approach is evaluated by a simplified model of a cantilever vibrating beam undergoing rubbing against a wall. The reduced model maintains accuracy while reducing the number of generalized coordinates compared to a linear manifold, resulting in less online computation time. However, the frequent update of the projection basis at each iteration imposes an extra online computational burden. REFERENCES [1] Rutzmoser, J.B., Rixen, D.J., Tiso, P. and Jain, S., 2017. Generalization of quadratic manifolds for reduced order modeling of nonlinear structural dynamics. Computers & Structures, 192, pp.196-209. [2] Yuan, J., El-Haddad, F., Salles, L., & Wong, C. (2019). Numerical assessment of reduced order modeling techniques for dynamic analysis of jointed structures with contact nonlinearities. Journal of Engineering for Gas Turbines and Power, 141(3), 031027.