Control of Lateral Vibrations and Slopes at Desired Locations Along Vibrating Beams

In the present paper we develop an exact approach to annihilate lateral vibrations and slopes at chosen locations in a vibrating beam subjected to an external excitation. The proposed scheme allows certain chosen points anywhere along the beam to remain stationary with zero slopes without using any rigid supports. This is beneficial because it would allow sensitive instruments to be placed near or at these points where the transverse vibrations and tilting are eliminated. In addition, when the locations of these desired points are in the vicinity of one another, it is possible to specify a region of nearly zero amplitude and zero slope, thus drastically reducing the level of vibration in that segment of the structure and preventing its rotation. This will be achieved by attaching a set of translational and/or rotational oscillators with calculated parameters at arbitrary selected locations along the beam. The proposed procedure develops an exact analytical scheme for choosing the required oscillators’ parameters utilizing the dynamic Green’s functions. An experimental setup, in which the vibrations of a clamped—clamped beam are measured using a laser vibrometer, was designed and the experimental measurements are compared with the analytical results. Sample of illustrative examples has been considered to verify the proposed method.