含新型减振元件的动力吸振器H_(∞) 优化设计方法

An approach to H_(∞)optimization design of dynamic vibration absorber with novel vibration attenuation elements

对于惯容器和负刚度元件组成的动力吸振器(DVA),其H_(∞)优化设计方法是该类新型动力吸振器应用的基础。基于该类吸振器的一阶状态空间运动方程和一种高效可靠的非光滑优化算法,在Matlab软件环境中直接对目标传递函数H_(∞)范数进行优化计算,目的在于给该类动力吸振器的优化设计提供一种简便高效的方法。该方法无需给出解析的目标函数,如主系统振幅放大因子和相对位移振幅放大因子等显式表达式,提出的双H_(∞)优化设计可同时降低该类吸振器中元件的相对位移振幅大小。以现有文献中两种典型的新型DVA为例,文中方法给出的数值优化结果与全局数值优化方法相同,优于固定点理论给出的解析结果。文中提出的双H_(∞)优化设计能在主系统振幅放大因子和相对位移振幅放大因子的优化上给出较好的折中方案,对该类吸振器的工程设计及应用具有重要的实际意义。

The H_(∞)optimization design method is the basis for the application of this new type of dynamic vibration absorber(DVA)composed of inertial containers and negative stiffness components.This paper presented an approach to minimizing H_(∞)norm of targeted transfer functions of the DVAs based on its first order state-space equations and an efficient non-smooth H_(∞)optimization algorithm under Matlab circumstance.Explicit formulas of various amplitude magnification factors to be optimized,such as those on the absolute and the relative displacements,need not be derived in the design procedure.The proposed dual H_(∞)optimization can simultaneously decrease the relative displacement amplitude magnification factor that may be larger in situation of single H_(∞)optimization.Two novel DVAs reported in the literature are taken as examples.For the first DVA,it gives the same optimal design parameters with those obtained from the global optimization numerical method,for the optimization of the amplitude magnification factor of the primary mass only;for the second DVA,it provides the optimal solutions while the analytical solutions derived by the so called fixed-points theory are not the optimal ones.The proposed dual H_(∞)optimization can provide the better compromises between the absolute displacements amplitude magnification factor of the primary mass and the relative displacements amplitude magnification factor for both novel DVAs,and has important practical significance for the engineering design and application of the novel vibration absorbers.