两自由度系统的动力吸振器参数最优化设计

Optimal Design of Parameters for Dynamic Vibration Absorber in Two-Degree-Freedom Systems

以附有动力吸振器的两自由度振动系统作为研究对象,利用达朗伯原理建立了数学模型,并进行无量纲化运算。针对动力吸振器的4个参数(κ,γ,δ,μ),综合运用变度量法中的Davidon-Fletcher-Powell(DFP)法、罚函数法、一维搜索法进行最优化设计,利用Matlab和Visual C++混合编程实现计算。计算结果表明:4个参数的收敛情况各有不同,γ和δ都趋于定义域的上限,而μ和κ则趋于一个定值。该结论对于在实际应用中合理设计动力吸振器的的参数、最大限度地抑制相关振动具有重要意义。

The two-degree-freedom vibration system made of the main mass and dynamic vibration absorber was studied. The mathematic model was built based on the principle of D＇Alembert theory which was calculated with non-dimensional equations. Aiming at four parameters （ κ,γ,δ,μ ） of the dynamic vibration absorber, the optimal design of parameters was processed with Davidon-Fletcher-Powell（DFP） method of variable metric, penalty function method and line-search method. The calculating methods were implemented by the program of Matlab and Visual C＋＋. The results show the convergence situations of four parameters. The parameters of γand δ tend towards the upper limit of the defining regions, whileμ and κ tend towards the fixed values respectively. The conclusion is significant to the parameters design of dynamic vibration absorber in actual application and controlling of the vibration.