2020 Volume 2020 Issue 65 Pages 59-68
This article presents exact algebraic solutions to optimization problems of a double-mass dynamic vibration absorber (DVA) attached to a viscously damped primary system. A series-type double-mass DVA was optimized using three optimization criteria (the H∞ optimization, H2 optimization, and stability maximization criteria), and exact algebraic solutions were successfully obtained for all of them. It is extremely difficult to optimize DVAs when there is damping in the primary system. Even in the optimization of the simpler single-mass DVA, exact solutions have been obtained only for the H2 optimization and stability maximization criteria. Because all actual vibration systems involve damping, the proposed expressions are expected to be useful in the design of DVAs. Furthermore, it is an important finding that the exact algebraic solutions exist even for such complex optimization problems of a linear vibration system.
