The Optimization of Damping of Four Configurations of a Vibrating Uniform Beam

Approximate analytical expressions for optimum damping for four configurations of forcing and damping a uniform beam were evaluated and the displacement responses for optimum damping values obtained from these expressions were calculated by a digital computer. It was found that the responses were accurately optimized. The sensitivity of maximum displacement response to deviation from optimum damping was investigated, but no analytical expressions relating change to deviation were obtained. An empirical formula, based upon consideration of the response of the beam as a single-degree-of-freedom system, was shown to be a good approximation of results obtained from the computer response curves. The four configurations investigated were relatively insensitive to changes in damping from optimum.