This paper presents the effect of friction-induced vibration between two beams in relative motion according to Timoshenko’s beam theory. This system is composed of two cantilever beams screwed together, allowing friction force to occur in the contact interface. The nonlinear behavior can be divided into two phases: stick and slip. The differential equations of motion in the two phases are developed, with the precision of the transition condition between each phase. A number of experiments are carried out in order to validate the theoretical model, the main contribution of which is to test these specimens in modes greater than one. The experiments demonstrate the influence of changing the clamping force on the stiffness of the structure and thus on its frequency and damping ratio. The comparison between theory and experiments reveals a good agreement. In addition, the tests show an increase in the modal damping ratio when the frequencies are increased. This leads to a considerable increase in energy dissipation by the structure, making it a good choice as a friction damper.