Optimum damping locations for structural vibration control

Abstract

A technique for determining the optimum damper locations and damping rates for a flexible structure has been developed. Using a nonlinear-mathematical-programming algorithm, a diagonal damping matrix is determined such that specified modes have a prescribed modal damping ratio. The design objective is to minimize the total damping effort while constraining the modal damping ratio to be equal or greater than the prescribed amount. Additional constraints require the diagonal elements of the damping matrix to be positive which guarantees that all modes of the damped system will be stable. Results are shown for a uniform free-free beam.