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

SU Ning, ZHANG Jie, HONG Ningning, PENG Shitao

Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (9) : 47-56.

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PDF(1979 KB)
Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (9) : 47-56.

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

  • SU Ning, ZHANG Jie, HONG Ningning, PENG Shitao
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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.

Key words

vibration control / inerter / dynamic vibration absorber / fixed-point theory / parameter optimization

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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

References

[1] Smith MC. Synthesis of mechanical networks: the Inerter[J]. IEEE Transactions on Automatic Control, 2002, 47: 1648-1662.
[2] Ma Ruisheng, Bi Kaiming, Hao Hong. Inerter-based structural vibration control: A state-of-the-art review[J]. Engineering Structures, 2021, 243: 112655.
[3] 张瑞甫, 曹嫣如, 潘超. 惯容减震(振)系统及其研究进展[J]. 工程力学, 2019, 36(10): 8-27. (Zhang Ruifu, Cao Yanru, Pan Chao. Inerter system and its state-of-the-art[J]. Engineering Mechanics, 2019, 36(10): 8-27. (in Chinese))
[4] Barredo E,  Larios JG, Colín J, et al. A novel high-performance passive non-traditional inerter-based dynamic vibration absorber[J]. Journal of Sound and Vibration, 2020, 485: 115583.
[5] Talley PC, Javidialesaadi A, Wierschem NE, et al. Evaluation of steel building structures with inerter-based dampers under seismic loading[J]. Engineering Structures, 2021, 242: 112488.
[6] 隋鹏, 申永军, 杨绍普. 一种含惯容和接地刚度的动力吸振器参数优化[J]. 力学学报, 2021, 53(5): 1412-1422.(Sui Peng, Shen Yongjun, Yang Shaopu. Parameters optimization of a dynamic vibration absorber with inerter and grounded stiffness[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1412-1422.(in Chinese))
[7] Den Hartog JP. Mechanical Vibrations[M]. New York: McGraw-Hall Book Company, 1947: 112-132
[8] Pietrosanti D, Angelis DM, Basili M. Optimal design and performance evaluation of systems with tuned mass damper inerter (TMDI) [J]. Earthquake Engineering and Structural Dynamics, 2017, 46: 1367–1388.
[9] Alotta G, Failla G. Improved inerter-based vibration absorbers[J]. International Journal of Mechanical Sciences, 2021, 192: 106087.
[10] Matteo DA, Masnata C, Pirrotta A. Simplified analytical solution for the optimal design of Tuned Mass Damper Inerter for base isolated structures[J]. Mechanical Systems and Signal Processing, 2019, 134: 106337.
[11] Dai Jun, Xu Zhaodong, Gai Panpan. Tuned mass-damper-inerter control of wind-induced vibration of flexible structures based on inerter location[J]. Engineering Structures, 2019, 199: 109585.
[12] Pietrosanti D, Angelis DM, Basili M. A generalized 2-DOF model for optimal design of MDOF structures controlled by Tuned Mass Damper Inerter (TMDI) [J]. International Journal of Mechanical Sciences, 2020, 185: 105849.
[13] Wang Zixiao, Giaralis A. Enhanced motion control performance of the tuned mass damper inerter through primary structure shaping[J]. Structural Control and Health Monitoring, 2021, 28(8): e2756.
[14] 苏宁, 彭士涛, 洪宁宁. 高耸烟囱结构调谐质量惯容阻尼器(TMDI)风振控制方法及效果研究[J]. 工程力学. doi: 10.6052/j.issn.1000-4750.2021.06.0490 (SU Ning, PENG Shitao, HONG Ningning. The wind-induced vibration control of high-rise chimneys by a tuned mass damper inerter (TMDI) [J]. Engineering Mechanics. doi: 10.6052/j.issn.1000-4750.2021.06.0490).
[15] Ren MZ, A variant design of the dynamic vibration absorber[J]. Journal of Sound and Vibration, 2001, 245(4): 762-770.
[16] Shen Yongjun, Xing Zhaoyang, Yang Shaopu, et al. Parameters optimization for a novel dynamic vibration absorber[J]. Mechanical Systems and Signal Processing, 2019, 133: 106282.
[17] 邢子康, 申永军, 李向红. 接地式三要素型动力吸振器性能分析. 力学学报[J]. 2019, 51(5): 1466-1475.(Xing Zikang, Shen Yongjun, Li Xianghong. Performance analysis of grounded three-element dynamic vibration absorber. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1466-1475. (in Chinese))
[18] Cheung YL, Wong WO. H2 optimization of a non-traditional dynamic vibration absorber for vibration control of structures under random force excitation[J]. Journal of Sound and Vibration, 2011, 330(6): 1039–1044.
[19] 李亚峰, 李寿英, 陈政清. 变化型惯质调谐质量阻尼器的优化与性能评价[J]. 振动工程学报, 2020, 33(5):877-884. (Li Yafeng, Li Shouying, Chen Zhengqing. Optimization and performance evaluation of variant tuned mass damper inerter[J]. Journal of Vibration Engineering, 2020, 33(5): 877-884. (in Chinese))
[20] Marian L, Giaralis A. Optimal design of a novel tuned mass-damper–inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems[J]. Probabilistic Engineering Mechanics, 2014, 38: 156-164.
[21] Zhu Zhiwen, Lei Wei, Wang Qinhua, et al. Study on wind-induced vibration control of linked high-rise buildings by using TMDI[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2020, 205: 104306.
[22] 王钦华, 雷伟, 祝志文, 等. 单重和多重调谐质量惯容阻尼器控制连体超高层建筑风振响应比较研究[J]. 建筑结构学报, 2021, 42(4): 25-34. (Wang Qinhua, Lei Wei, Zhu Zhiwen, et al. Comparison of mitigation effects on wind-induced response of connected super-high-rise buildings controlled by TMDI and MTMDI[J]. Journal of Building Structures, 2021, 42(4): 25-34. (in Chinese)).
[23] Giaralis A, Taflanidis AA. Optimal tuned mass-damper-inerter (TMDI) design for seismically excited MDOF structures with model uncertainties based on reliability criteria[J]. Structural Control and Health Monitoring, 2017, 25(2): e2082
[24] Ruiz R, Taflanidis AA, Giaralis A, et al. Risk-informed optimization of the tuned mass-damper-inerter (TMDI) for the seismic protection of multi-storey building structures[J]. Engineering Structures, 2018, 177: 836-850.
[25] Asami T, Nishihara O, Baz AM. Analytical solutions to H∞ and H2 optimization of dynamic vibration absorbers attached to damped linear systems[J]. Journal of Vibration and Acoustics, 2002, 124 (2) 284-295.
[26] Spanos PD, Miller SM. Hilbert transform generalization of a classical random vibration integral. Journal of Applied Mechanics, 1993, 61(3): 575-581.
[27] Su Ning, Cao Zhenggang, Wu Yue. Fast frequency domain algorithm to estimate the dynamic wind-induced response on large-span roofs based on Cauchy’s residue theorem[J]. International Journal of Structural Stability and Dynamics, 2018, 18(3): 1850037.
[28] Su Ning, Peng Shitao, Hong Ningning. Universal simplified spectral models and closed form solutions to the wind-induced responses for high-rise structures[J]. Results in Engineering, 2021, 10: 100230.
[29] Tiwari ND, Gogoi A, Hazra B, et al. A shape memory alloy-tuned mass damper inerter system for passive control of linked-SDOF structural systems under seismic excitation[J]. Journal of Sound and Vibration, 2021, 494: 115893.
[30] Wang Qinhua, Tiwari ND, Hazra B, et al. MTMDI for mitigating wind-induced responses of linked high-rise buildings[J]. Journal of Structural Engineering, 2021, 147(4): 1-8.
[31] Wang Qinhua, Qiao Haoshuai, Domenico DD, et al. Seismic response control of adjacent high-rise buildings linked by the Tuned Liquid Column Damper-Inerter (TLCDI) [J]. Engineering Structures, 2020, 223: 111169.
[32] 莊初立, 五十子幸树, 张永山. 极端地震下惯容器-弹簧-阻尼装置对隔震结构减震效果研究[J]. 振动与冲击, 2019, 38(12): 112-117.(CHONG Cholap1,KOHJU Ikago2,ZHANG Yongshan1. Effectiveness of an inerter-spring-damper device in the seismic response control of a isolated structure under extreme earthquakes. Journal of Vibration and Shock, 2019, 38(12): 112-117. (in Chinese))
[33] 王勇,汪若尘,孟浩东,张步云. 基于相对加速度-相对速度控制的半主动惯容隔振器动态特性研究[J]. 振动与冲击, 2019, 38(21): 194-201. (WANG Yong1,2,WANG Ruochen1, MENG Haodong3, ZHANG Buyun1. Dynamic characteristics of semi active inerter-based vibration isolator with relative acceleration-relative velocity control. Journal of Vibration and Shock, 2019, 38(21): 194-201. (in Chinese))
[34] 高科. 港口高耸烟囱风荷载的风洞试验研究及中美规范对比[J]. 水道港口, 2020, 41(6): 675-681. (Gao Ke. Wind tunnel study on wind load of Port high-rise chimney and comparisons with China and US codes. Journal of Waterway and Harbor, 2020, 41(6): 675-681. (in Chinese))
[35] Kiureghian DA, Neuenhofer A. Response spectrum method for multi-support seismic excitations. Earthquake Engineering and Structural Dynamics, 1992, 21: 713–740.
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