Dynamics of Cantilever Beams due to Time-Dependent Excitations and their Suppression

A Fourier Transform method is applied to determine the displacements of a cantilever beam subjected to a multi-frequency excitations at the base. To dampen the displacements of the beam, a point mass is attached to the beam. The position of the mass on the beam is determined such that the overall deflections of the beam are minimal. It is shown that these attachments to the beam are effective in reducing the vibrations of the beam but their position is frequency dependent. It is shown that the low frequency component of the external excitation is most important in finding the optimal position of the mass.