Numerical solutions for optimal double-mass dynamic vibration absorbers attached to a damped primary system

Abstract

Because double-mass dynamic vibration absorbers (DVAs) are superior to single-mass DVAs in terms of their vibration suppression performance and robustness, they have been increasingly studied recently. The optimization of double-mass DVAs is much more difficult than that of single-mass DVAs. However, recently, the ability of formula manipulation solvers typified by Mathematica has greatly improved, and exact algebraic solutions have been obtained for double-mass DVAs. The optimal solution for a double-mass DVA attached to a damped primary system has been reported in the form of an exact algebraic solution in a previous report. That paper reported the algebraic optimal solutions for a series-type double-mass DVA for the compliance and mobility transfer functions of the primary system successfully obtained by applying three different optimization criteria: H∞ optimization, H2 optimization, and stability maximization. In the present article, the numerical solutions to optimization problems for double-mass DVAs that cannot be algebraically solved are presented. There are two types of double-mass DVAs: series- and parallel-type DVAs. When applying the three optimization criteria mentioned above to each of them, there exist a total of 22 different optimal solutions because there are three transfer functions— the compliance, mobility, and accelerance transfer functions—that are typically used to describe the absolute response of the primary system. Of these 22 solutions, 10 solutions for the compliance transfer function are introduced in this article.

Keywords

• vibration
• optimal design
• double-mass dynamic vibration absorbers
• h∞ optimization criterion
• h2 optimization criterion
• stability maximization criterion
• damped primary system