Optimal Design of Double-Mass Dynamic Vibration Absorbers Arranged in Series or in Parallel

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, the H_∞ optimization, H₂ optimization, and stability maximization criteria, were considered for the design of the DVAs, and a performance index was defined for each of these criteria. 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 non-negative, the optimal value 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 equations. Second, the performance of these DVAs was compared with a single-mass DVA. The result 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. Finally, a procedure for deriving the algebraic or numerical solutions for H₂ optimization is described. The derivation procedure of other optimal solutions will be introduced in the future paper.