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The presented research discusses the coupled flexural-torsional vibrations of a thin walled composite box beam made of a ply composite material attached to a rotating hub. The observed coupling between flexural and torsional modes is resulting from the directional properties of the composite material with assumed a priori fibers’ orientation. Moreover, several non-classical effects like shear deformation, cross-sectional rotatory inertia and driving hub inertia are taken into account. Based on authors previous research a system of partial differential equations for the discussed structure is given. Next, this system is solved and the eigenvalues and eigenmodes are obtained by the Extended Galerkin method. A simple parametric analysis of hub’s inertia impact on systems dynamic characteristics is performed by considering aluminium and steel hub design. Within this analysis resonance curves obtained for excited vibrations have been plotted. Next, graphs representing natural frequencies of the beam-hub system against hub’s mass moment of inertia are shown. Finally, time histories of the transversal displacement,shear deformation angle and twist angle are given for both considered rotor assembly variants.