Tuned mass absorbers on damped structures under random load

A substantial literature exists on the optimal choice of parameters of a tuned mass absorber on a structure excited by a force or by ground acceleration with random characteristics in the form of white noise. In the absence of structural damping the optimal frequency tuning is determined from the mass ratio alone, and the damping can be determined subsequently. Only approximate results are available for the influence of damping in the original structure, typically in the form of series expansions. In the present paper it is demonstrated that for typical mass ratios in the order of a few percent the classic stochastic frequency tuning gives the same standard deviation of the response amplitude within a margin of 0.001 as when using the classic frequency tuning for harmonic load variation, and then optimizing the damping separately. Simple approximate, but very accurate, expressions are obtained for the response variance of a structure with initial damping in terms of the mass ratio and both damping ratios. Within this format the optimal tuning of the absorber turns out to be independent of the structural damping, and a simple explicit expression is obtained for the equivalent total damping.