Free vibrations of uniform Timoshenko beams with attachments

The problem of free transverse vibrations of Timoshenko beams with attachments like translational and rotational springs, concentrated mass including the moment of inertia, linear undamped oscillators and additional supports is considered. The frequency equation for the combined system is derived by means of the Lagrange multiplier formalism. The exact solution of the free vibration problem of the beam without attachments is taken into account for the formulation of the free vibration problem of the combined system. Numerical examples show the separate or coupling influences of the additional elements on the combined system's frequencies. The comparison of results obtained by using the present approach with results of the exact solution indicates a good agreement.