Exact Algebraic Solution of an Optimal Double-Mass Dynamic Vibration Absorber Attached to a Damped Primary System
Exact Algebraic Solution of an Optimal Double-Mass Dynamic Vibration Absorber Attached to a Damped Primary System
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连接到阻尼主系统的最佳双质量动态减振器的精确代数解
DOI：
10.1115/1.4043815
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Toshihiko Asami
中科院分区：
文献类型：
--
作者：
Itsuro Honda;Toshihiko Asami and Hidetaka Shiozaki;Toshihiko Asami;浅見 敏彦;浅見 敏彦，水川 凱斗，山田 啓介;Toshihiko Asami
本文给出了粘滞阻尼主系统双质量动力吸振器（DVA）优化问题的精确代数解。采用H∞优化、H2优化和稳定性最大化3种优化准则对串联型双质量DVA进行了优化，均获得了精确的代数解。当主系统中存在阻尼时，优化DVA是极其困难的。即使在简单的单质量DVA的优化，精确的解决方案已获得仅为H2优化和稳定性最大化的标准。对于H∞优化问题，只得到了数值解和近似摄动解.关于双质量DVA，在本研究中，在并联型DVA连接到阻尼主系统的情况下，无法获得精确的代数解。对于串联型双质量DVA，这是本研究的重点，一个精确的代数解得到的力激励系统，其中的干扰力直接作用在主质量;然而，一个代数解没有得到的运动激励系统，其中的基础系统进行周期性位移。由于所有实际的振动系统涉及阻尼，在这项研究中获得的结果是有用的实际DVA的设计。此外，它是一个很大的惊喜，精确的代数解存在，即使是这样复杂的优化问题的线性振动系统。
This article presents exact algebraic solutions to optimization problems of a double-mass dynamic vibration absorber (DVA) attached to a viscous damped primary system. The series-type double-mass DVA was optimized using three optimization criteria (the H∞optimization, H2optimization, and stability maximization criteria), and exact algebraic solutions were successfully obtained for all of them. It is extremely difficult to optimize DVAs when there is damping in the primary system. Even in the optimization of the simpler single-mass DVA, exact solutions have been obtained only for the H2optimization and stability maximization criteria. For H∞optimization, only numerical solutions and an approximate perturbation solution have been obtained. Regarding double-mass DVAs, an exact algebraic solution could not be obtained in this study in the case where a parallel-type DVA is attached to the damped primary system. For the series-type double-mass DVA, which was the focus of the present study, an exact algebraic solution was obtained for the force excitation system, in which the disturbance force acts directly on the primary mass; however, an algebraic solution was not obtained for the motion excitation system, in which the foundation of the system is subjected to a periodic displacement. Because all actual vibration systems involve damping, the results obtained in this study are expected to be useful in the design of actual DVAs. Furthermore, it is a great surprise that an exact algebraic solution exists even for such complex optimization problems of a linear vibration system.