Optimal damper location for randomly forced cantilever beams

The work reported here considers the attachment of a viscous damper to a cantilever beam that is driven by temporally white noise with several different spatial distributions. The variables in the problem to be optimized are the location and the value of the damper. For each of the spatial distributions, there is a location and damper value that will minimize the mean square motion averaged over the beam length. These minima are shown to be not a strong function of the spatial distribution of the forcing function with the best location being at 70% of the length from the fixed end. The optimal value of the damper is shown to be 50 times the product of the beam mass and the first radian natural frequency for the beam.