The vibration absorber has been used in many applications since invented. In the case of vibration control by the tuned mass damper (TMD), the selection of optimum absorber parameters is extremely important. This paper presents a closed-form expression for the optimum tuning ratio of a TMD attached to a damped primary system. The result is obtained by using equivalent linearization method. The values of the optimum tuning ratio derived from the expression proposed in this paper have been compared with those obtained numerically as well as the results obtained from other authors. These values are reliable even the mass ratio of TMD to the primary structure and the structural damping ratio are quite high. A simulation study has also been carried out to illustrate the obtained results.

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The Voigt-type of dynamic vibration absorber is a classical model and has attracted considerable attention in many years because of its simple design, high reliability and useful applications in the fields of civil and mechanical engineering. Recently, a non-traditional type of dynamic vibration absorber was proposed. Unlike the traditional damped absorber configuration, the non-traditional absorber has a linear viscous damper connecting the absorber mass directly to the ground instead of the main mass. There have been some studies on the design of the non-traditional dynamic vibration absorber in the case of undamped primary structures. Those studies have shown that the non-traditional dynamic vibration absorber has better performance than the traditional dynamic vibration absorber. However, when damping is present at the primary system, there are very few studies on the design of non-traditional dynamic vibration absorber. This article presents a simple approach to determine the approximate analytical solutions for the [Formula: see text] optimization of the non-traditional dynamic vibration absorber attached to the damped primary structure subjected to force excitation. The main idea of the study is based on the dual criterion suggested by Anh in order to replace approximately the original damped structure by an equivalent undamped structure. Then the approximate analytical solution of dynamic vibration absorber’s parameters is given by using known results for undamped structure obtained. The comparisons have been done to verify the effectiveness of the obtained results.