Optimal design of a series-type double-mass hysteretically damped dynamic vibration absorber based on the stability criterion

Abstract

In most dynamic vibration absorbers (DVAs) used in practical applications, polymeric materials that have both restoring capabilities and damping effects are used instead of coil springs as spring elements. It is known that the damping force for such polymeric materials has hysteretic characteristics and varies in proportion to the relative displacement rather than the relative velocity between objects. This paper proposes an optimal design formula for a double-mass hysteretically damped DVA with two masses connected in series. For the design of the DVA in this study, the stability maximization criterion, which attenuates the free-vibration response of the primary system in the shortest time, was adopted. It was found that the optimal design expression for installing the series-type double-mass DVA on an undamped primary system can be expressed by a very simple formula. The maximized stability, which determines the speed of vibration convergence, of the double-mass DVA was 1.7 times that of the corresponding single-mass DVA. When there is damping in the primary system, the optimal design condition for the DVA cannot be expressed with such a simple formula, but an equation to calculate it is presented in this paper. The equation can be easily solved numerically, and the results show that the stability of the system is further increased compared to the undamped primary system.

Keywords

• vibration
• optimal design
• transient vibration
• hysteretically damped dynamic vibration absorber
• series-type double-mass absorber
• stability maximization criterion
• damped primary system