Calculation of the H∞ optimized design of a single-mass dynamic vibration absorber attached to a damped primary system

Abstract

There are three criteria typically used in the design of dynamic vibration absorbers (DVAs): H∞ optimization, H2 optimization, and stability maximization. Recently, interest has shifted to the optimization of multi-mass DVAs, but in fact, in even the most basic single-mass DVA, the effect of primary system damping on the optimal solution is still not fully understood with respect to the H∞ criterion. The author has recently reported an exact H∞-optimal solution for a series-type double-mass DVA attached to a damped primary system. This article presents the application of this H∞ optimization method developed for a double-mass DVA to the optimization of a single-mass DVA. In the H∞ optimization of the mobility transfer function, a highly accurate numerical solution was successfully obtained by solving a single sixth-order algebraic equation. In the case of the optimization of the compliance and accelerance transfer functions, it is shown that a highly accurate numerical solution can be obtained by solving ternary systems of simultaneous algebraic equations. It should be noted that the equations presented in this paper can be factorized into simpler equations when there is no damping in the primary system. It is also demonstrated herein that the factorized expressions yield the previously published H∞-optimal solutions.

Keywords

• dynamic vibration absorber
• damped primary system
• h∞ optimization
• formula manipulation
• exact algebraic equation
• compliance transfer function
• mobility and accelerance functions