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An analytical model for the vibration response of a curved beam is developed and presented. The model is based on the solution (closed solution) of the dynamic differential equations of equilibrium for an infinitesimal element vibrating out of its initial plane of curvature and allows for inclusion of the effects of rotary inertia and or shear deformation. Final solutions are presented under the form of elements of the tip dynamic stiffness matrix for a free-free beam. The validity of the model is assessed by comparison of theoretical and experimental results for several examples of curved beams.