广义变式惯容动力吸振器的H&infin;和H2解析优化

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (9) : 47-56.

论文

广义变式惯容动力吸振器的H∞和H2解析优化

苏宁，张杰，洪宁宁，彭士涛

作者信息 +

H∞ and H2 optimization solutions to generalized variant inerter-enhanced DVA

SU Ning, ZHANG Jie, HONG Ningning, PENG Shitao

Author information +

文章历史 +

摘要

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，本文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H2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，采用本文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。本文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。

Abstract

In order to achieve an excellent vibration control performance under installation restrictions, the optimal design and performance evaluation of generalized variant inerter-enhanced dynamic vibration absorbers that can be connected to arbitrary locations on the primary vibration system are investigated. Based on the principle of virtual work, the differential equation of motion and a uniform frequency response function with seven parameters are established on a generalized single-degree-of-freedom primary vibration system, which can be applied on a variety of inerter enhanced dynamic vibration absorbers. The analytic solutions of H∞ optimization on these inerter enhanced dynamic vibration absorbers are derived based on the fixed-point theory. Moreover, the analytic solutions to the uncontrolled and controlled dynamic responses of the primary vibration system subjected white noise load and base excitations are obtained through an analog filter approach. Based on the parametric analysis results, a simplified empirical formula of H2 optimization results are fitted. Through a case study on the wind and seismic induced vibration control of a slender chimney, the presented empirical formula is proved to be applicable for the optimal design of a fundamental mode dominant structure subjected to stochastic excitations. The relative errors between the optimal control ratios estimated by the empirical formulas of optimal parameters and numerical analysis are within 2%, which can be well accepted in engineering practices. The presented results can provide guidance for the engineering optimal design of generalized variant inerter-enhanced dynamic vibration absorbers. And the research framework is also promise to provide a reference for the optimization studies on other dynamic vibration absorbers.

导出引用

苏宁，张杰，洪宁宁，彭士涛. 广义变式惯容动力吸振器的H∞和H2解析优化[J]. 振动与冲击, 2023, 42(9): 47-56

SU Ning, ZHANG Jie, HONG Ningning, PENG Shitao. H∞ and H2 optimization solutions to generalized variant inerter-enhanced DVA[J]. Journal of Vibration and Shock, 2023, 42(9): 47-56

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