Design of three-element dynamic vibration absorber for damped linear structures

The standard type of dynamic vibration absorber (DVA) called the Voigt DVA is a classical model and has long been investigated. In the paper, we will consider an optimization problem of another model of DVA that is called three-element type DVA for damped primary structures. Unlike the standard absorber configuration, the three-element DVA contains two spring elements in which one is connected to a dashpot in series and the other is placed in parallel. There have been some studies on the design of the three-element DVA for undamped primary structures. Those studies have shown that the three-element DVA produces better performance than the Voigt DVA does. When damping is present at the primary system, to the best knowledge of the authors, there has been no study on the three-element dynamic vibration absorber. This work presents a simple approach to determine the approximate analytical solutions for the H ∞ optimization of the three-element DVA attached to the damped primary structure. The main idea of the study is based on the criteria of the equivalent linearization method in order to replace approximately the original damped structure by an equivalent undamped one. Then the approximate analytical solution of the DVAʹs parameters is given by using known results for the undamped structure obtained. The comparisons have been done to verify the effectiveness of the obtained results.