H_∞規範とH₂規範に基づくヒステリシス減衰型動吸振器の最適設計

抄録

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. On the other hand, many DVAs used for practical use are made of polymeric rubber materials having both restorative and damping effects. The damping force of this polymer material is considered to have a hysteretic type damping characteristic that is proportional to the displacement, not the velocity of the object. However, there are very few studies on the optimal design of this hysteretic damped DVA, and at present the design formula of the well-known general viscous damped DVA is used for design of this type of DVA. This article reports the optimal solution of this hysteretic damped DVA. For generality, it is assumed that the primary system also has a structural damping that can be treated as a hysteretic damping. Two criteria, namely H∞ and H criteria, are adopted for the optimization of DVA. For the former, we succeeded in deriving an exact algebraic solution, and for the latter we showed the simultaneous equations and its numerical solution.