A quasi-optimal design formula of a parallel-type double-mass dynamic vibration absorber based on the stability criterion

Abstract

In recent years, many researchers have been attempting to optimize multi-mass dynamic vibration absorbers (DVAs) to improve the performance and robustness. To date, exact design formulas have been obtained for series-type double-mass DVAs, but for parallel-type double-mass DVAs, the optimal solutions have only been obtained in numerical form. Moreover, the expressions for calculating the numerical solutions were extremely long, making it impossible for the average user to obtain accurate design values. Another problem with the previously published expressions is that their length amplifies the rounding errors under certain calculation conditions, and sometimes makes the calculations impossible. In this paper, we propose an approximate design formula for a parallel-type double-mass DVA that is almost comparable to the exact solution in terms of accuracy. The deterioration rate of the damping performance has been confirmed as less than 0.015% in the typical use range of DVAs (mass ratio with the primary system of less than 0.2).

Keywords

• vibration
• optimal design
• double-mass dynamic vibration absorber
• parallel-type absorber
• stability criterion
• damped primary system
• triple characteristic root
• algebraic manipulation