广义变式惯容动力吸振器的H_(∞)和H_(2)解析优化

H_(∞) and H_(2) optimization solutions to generalized variant inerter-enhanced DVA

为使动力吸振器(dynamic vibration absorber,DVA)在连接限制的条件下充分发挥振动控制性能,研究了可连接在主振动系统任意位置的广义变式惯容动力吸振器的参数优化及其控制效果。基于虚功原理,在广义单自由度的主振动系统上,建立了适用于多种惯容动力吸振器的运动微分方程以及七参数通用频响函数。在此基础上,基于固定点理论推导得到了上述动力吸振器的H_(∞)优化解析解。并通过滤波理论得到了白噪声力和基础激励下的动力响应解析解,基于大量参数分析结果,拟合得到了H_(2)优化的简化计算经验公式。经高耸烟囱结构的风致振动和地震响应控制算例验证,采用提出的经验公式对随机激励下的一阶振动主导的结构进行振动控制优化设计,最优控制比误差在2%以内,具有良好的工程适用性。该文章的分析结果可为广义变式惯容动力吸振器的工程设计提供理论依据,分析流程也可为其他类型动力吸振器的振动控制优化研究提供参考。

Here,to give full play to vibration control performance of dynamic vibration absorber(DVA)under the condition of connection restriction,parameter optimization and control effect of generalized variant inerter-enhanced DVA being able to be connected at any position of a main vibration system were studied.Based on the principle of virtual work,on a generalized single-DOF main vibration system,differential equations of motion and 7-parameter universal frequency response function applicable to various inerter-enhanced DVAs were established.Then,based on the fixed point theory,the H_(∞)optimization analytic solution to the above DVA was obtained through derivation.Analytic solutions to dynamic responses under white noise load and foundation excitation were obtained by using filtering theory.Based on a large number of parametric analysis results,a simplified calculation empirical formula for H_(2) optimization was obtained by fitting.Examples of wind-induced vibration control and seismic response control for a high-rise chimney structure showed that if the empirical formula proposed here is used to do optimization design for vibration control of a structure dominated by its first-order modal vibration under random excitation,the error of the optimal control ratio is within 2%to reveal good engineering applicability;the study results can provide a theoretical basis for engineering design of generalized variant inerter-enhanced DVA;the analysis process can also provide a reference for vibration control optimization studying of other type DVAs.