Optimal design of a hysteretically damped dynamic vibration absorber

Abstract

In the optimization of dynamic vibration absorbers (DVAs), it is generally assumed that the damping force changes in proportion to the velocity of the object; this damping is called viscous damping. However, many DVAs used in practical applications are made of polymeric rubber materials having both restorative and damping effects. This polymer material is considered to show a hysteretic damping force that is proportional to the displacement rather than the velocity of the object. Despite the widespread use of such hysteretically damped DVAs, there are very few studies on their optimal design, and the design formula of the well-known general viscously damped DVA is presently used for the design of this type of DVA. This article reports the optimal solution of this hysteretically damped DVA. For generality, it is assumed that the primary system also has structural damping that can be treated as hysteretic damping. Three optimization criteria, namely the H∞ optimization, H2 optimization, and stability maximization criteria, were adopted for the optimization of the DVA. For the H∞ optimization and stability maximization criteria, exact algebraic solutions were successfully derived, and for the H2 criterion, simultaneous equations with six unknowns and their numerical solutions were obtained.

Keywords

• vibration
• optimal design
• hysteretically damped dynamic vibration absorber
• h∞ optimization criterion
• h2 optimization criterion
• stability maximization criterion
• damped primary system