Abstract: For a single degree of freedom damped system with dynamic vibration absorbers(DVA), we studied a correct mobility matrix of the system on the basis of structure mobility theory in this paper. In addition, the expressions of the total power flow input from vibration sources to the system, the power flow transmitted to the main vibration system and the power flow absorbed by DVA were analyzed. Furthermore, in the paper the control mechanism of DVA on the transmission characteristics of the power flow was revealed. Finally, an approach to the optimum design of DVA was proposed in which the power flow was made the control object, and the ordonnance relations among the optimum parameters of DVA were provided.