一种含惯容的接地刚度时滞反馈动力吸振器的多目标优化设计  

Multi-objective optimization design of a grounded stiffness time delay feedback dynamic vibration absorber with inerter

作　　者：杨柳青 赵艳影[1] YANG Liuqing;ZHAO Yanying(School of Aircraft Engineering,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学飞行器工程学院,南昌330063

出　　处：《振动与冲击》2023年第23期133-143,共11页Journal of Vibration and Shock

基　　金：国家自然科学基金(12072140);江西省自然科学基金重点项目(20202ACBL201003)。

摘　　要：惯容和接地刚度可以通过改变振动系统的固有频率对系统的一部分振动起到抑制作用,在被动控制系统中耦合时滞反馈主动控制是一种相对操作简单且有效的振动主动控制技术。通过对含惯容的接地刚度时滞反馈动力吸振器系统进行多目标优化设计,通过对系统结构参数和控制参数进行优化,实现了对主系统共振峰幅值、反共振峰幅值、反共振频带对称性的有效控制;首先,通过固定点理论得到接地刚度系统的最优结构参数;其次,通过特征根的簇处理(cluster treatment of characteristic roots, CTCR)方法对控制系统进行稳定性分析,得到振动系统稳定的反馈增益系数和时滞控制参数的稳定区域;再次,在满足优化准则的前提下,根据反共振频带的对称性得到最优惯容比;最后,结合最优结构参数和准则,得到满足优化目标的控制参数区域。研究表明,针对任意一个外激励频率,在控制参数区域内存在一对反馈增益系数和时滞的最优参数,能够将主系统的振幅抑制到最小值;幅频响应曲线和时间历程响应曲线的数值模拟结果与解析结果吻合,证明了结果的可靠性;研究结果为时滞主动控制动力吸振器的优化和设计提供了理论依据。Inerter and grounded stiffness can suppress a portion of a system’s vibration by changing the system’s natural frequency.A passive control system coupled by a time-delay feedback active control is a relatively simple and effective vibration active control technology.Here,multi-objective optimization design for a grounded stiffness time delay feedback dynamic vibration absorber system with inerter was performed,and the system’s structure parameters and control parameters were optimized to realize effective control of the main system’s resonance peak amplitude,anti-resonance peak amplitude and anti-resonance frequency band symmetry.Firstly,the optimal structural parameters of the grounded stiffness system were obtained with the fixed-point theory.Secondly,the stability analysis of the control system was performed using the cluster treatment of characteristic roots(CTCR)method to obtain the vibration system’s stable feedback gain coefficients and stable regions of time delay control parameters.Furthermore,under the premise of meeting optimization criteria,the optimal inerter ratio was obtained based on the symmetry of the anti-resonance frequency band.Finally,by combining the optimal structural parameters and criteria,control parameter regions meeting optimization objectives were obtained.Results showed that for any external excitation frequency,there are a pair of feedback gain coefficients and time delay’s optimal parameters in control parameter region to suppress main system amplitude to the minimum value;the numerical simulation results of the system’s amplitude-frequency response curve and time history response curve agree well with analytical solution results to verify the reliability of the results obtained here;the results can provide a theoretical basis for optimization and design of time-delay active control dynamic vibration absorbers.

关 键 词：动力吸振器 惯容 接地刚度 时滞反馈控制 多目标优化 

分 类 号：O328[理学—一般力学与力学基础] TH213.3[理学—力学]