Abstract
This paper considers the optimal design of double-mass dynamic vibration absorbers (DVAs) attached to an undamped single-degree-of-freedom system. Three different optimization criteria (H∞ optimization, H2 optimization, and stability maximization criteria) were considered for the design of the DVAs. First, the analytical models of vibratory systems with double-mass DVAs were considered, and seven dimensionless parameters were defined. Five of these parameters must be optimized to minimize or maximize the performance indices. Assuming that all dimensionless parameters are nonnegative, the optimal values of one parameter for a double-mass DVA arranged in series (series-type DVA) was proven to be zero. The optimal adjustment conditions of the other four parameters were derived as simple algebraic formulae for the H2 and stability criteria and numerically determined for the H∞ criterion. For a double-mass DVA arranged in parallel (parallel-type DVA), all five parameters were found to have nonzero optimal values, and these values were obtained numerically by solving simultaneous algebraic equation for each of the optimization criteria. Second, a comparison of the optimized values of the performance indices revealed that for all optimization criteria, the performance of the series-type DVA is the best among the three DVAs and that of the single-mass DVA is the worst.
