基于振幅放大机制的周期钢弹簧浮置板轨道结构低频振动控制

doi:10.3901/JME.2024.03.155

摘要/Abstract

摘要： 钢弹簧浮置板轨道结构因其具有良好的减隔振性能在城市轨道交通中应用广泛,但对于 20 Hz 以下的低频振动,尤其是人体敏感频率范围内(4~8 Hz)的隔振效果并不理想。鉴于此,引入振幅放大思想,设计了一种杠杆式隔振器,用于有效提升钢弹簧浮置板轨道在人体敏感频率范围内的隔振效果。基于钢弹簧浮置板轨道结构的周期性特征,采用能量泛函变分法并结合人工弹簧技术建立了配置有杠杆式隔振器的周期性钢弹簧浮置板轨道结构带隙特性分析模型;以带隙特性作为评价指标,从研究振动波传递的角度出发,系统地分析了配置有杠杆式隔振器的钢弹簧浮置板轨道结构中弯曲振动波的传递路径特征,验证了杠杆式隔振器对轨道结构中低频弯曲振动波的调控作用。在此基础上,进一步考虑列车荷载的作用,分析验证了动态轮轨力作用下杠杆式隔振器的低频隔振性能以及对轨道结构动力响应的影响。结果表明:杠杆式隔振器对浮置板轨道的低频弯曲波调控效果明显,由 0~9.6 Hz 成功调控至 4 Hz 以下;与普通浮置板轨道相比, 4~8 Hz 范围内传递至下部基础的力大幅度衰减,最大衰减约 20 dB,同时,杠杆式隔振器对轨道结构的振动也有一定的抑制效果。

关键词: 振幅放大, 周期性钢弹簧浮置板轨道, 带隙, 弯曲波调控, 低频振动控制

Abstract: Steel spring floating slab track structures are widely used in urban rail transport due to their excellent vibration damping performance. However, the vibration isolation effect could be better for low frequency vibrations below 20 Hz, especially in the human body-sensitive frequency range (4 to 8 Hz). Given this, a lever-type vibration isolator has been designed to effectively improve the vibration isolation of steel spring floating slab tracks in the human-sensitive frequency range by introducing the idea of amplitude amplification. Based on the periodic characteristics of steel spring floating slab track structures, an analytical model of the band gap characteristics of periodic steel spring floating slab track structures equipped with lever-type vibration isolators is developed using the energy-generalized variational method combined with artificial spring technology. The transmission path characteristics of flexural vibration waves in steel spring floating slab track structures equipped with lever-type vibration isolators are systematically analyzed from the perspective of vibration wave transmission by using the band gap characteristics as an evaluation index. Regulation of low frequency flexural vibration waves in track structures by lever-type vibration isolators is verified. On this basis, the low frequency vibration isolation performance of lever-type vibration isolators under dynamic wheel-rail forces and the effect on the dynamic response of the track structure are analyzed and verified. The results indicate that:the lever-typ vibration isolator has obvious control effect on the low-frequency flexural wave of the floating slab track, which is successfully regulated from 0~9.6 Hz to below 4 Hz. Compared with the ordinary floating slab track, the force transmitted to the lower foundation in the range of 4~8 Hz is greatly attenuated, and the maximum attenuation is about 20 dB. At the same time, the lever vibration isolator also has a certain suppression effect on the vibration of the track structure.

Key words: amplitude amplification, periodic steel spring floating slab track, band gap, flexural wave regulation, low frequency vibration control

中图分类号:

U211
O328

冯青松, 杨舟, 郭文杰. 基于振幅放大机制的周期钢弹簧浮置板轨道结构低频振动控制[J]. 机械工程学报, 2024, 60(3): 155-169.

FENG Qingsong, YANG Zhou, GUO Wenjie. Low Frequency Vibration Control of Periodic Steel Spring Floating Slab Track Based on Amplitude Amplification Mechanism[J]. Journal of Mechanical Engineering, 2024, 60(3): 155-169.

参考文献

[1] 杨吉忠,颜华,魏永幸,等.基于TRIZ理论的低频减振轨道结构研究[J].铁道工程学报, 2015, 32(4):60-64. YANG Jizhong,YAN Hua,WEI Yongxing,et al. Research on the low frequency vibration attenuation in track structure based on TRIZ theory[J]. Journal of Railway Engineering Society, 2015, 32(4):60-64.
[2] 刘维宁,丁德云,李克飞,等.钢弹簧浮置板轨道低频特征试验研究[J].土木工程学报, 2011, 44(8):118-125. LIU Weining, DING Deyun, LI Kefei, et al. Experimental study of the low-frequency vibration characteristics of steel spring floating slab track[J]. China Civil Engineering Journal, 2011, 44(8):118-125.
[3] JIANG Bolong, MA Meng, LI Minghang, et al. Experimental study of the vibration characteristics of the floating slab track in metro turnout zones[J]. Proceedings of the Institution of Mechanical Engineers Part-F:Journal of Rail and Rapid Transit, 2019, 233(10):1081-1096.
[4] LEI Xiaoyan, JIANG Chongda. Analysis of vibration reduction effect of steel spring floating slab track with finite elements[J]. Journal of Vibration and Control,2016, 22(6):1462-1471.
[5] 梁瑞华,马蒙,刘卫丰,等.考虑地层动力特性差异的减振轨道减振效果评价[J].工程力学, 2020, 37(增刊1):75-81. LIANG Ruihua, MA Meng, LIU Weifeng, et al. Evaluation of vibration mitigation effect of vibration isolated track considering stratum dynamic characteristics difference[J]. Engineering Mechanics, 2020, 37(Suppl 1):75-81.
[6] CUI Xiaolu, CHEN Guangxiong, YANG Honggang, et al. Study on rail corrugation of a metro tangential track with Cologne-egg type fasteners[J]. Vehicle System Dynamics, 2016, 54(3):353-369.
[7] STUART L G, JOHN W E. Development of corrugation as a result of varying normal load[J]. Wear, 2008, 265(9):1150-1155.
[8] LOJDA V, BELKOM A V, KREJCIRIKOVA H. Investigation of the elastic modulus of polymer sleepers under a quasistatic and cyclic loading[J]. Civil Environmental Engineering, 2019, 15(2):125-133.
[9] 韩健,李志辉,肖新标,等.地铁列车-嵌入式轨道系统动力学性能研究I:理论建模、试验分析及验证[J].机械工程学报, 2020, 56(22):148-158. HAN Jian, LI Zhihui, XIAO Xinbiao, et al. Study on dynamic behaviour of metro train and embedded track system I:Theoretical modeling, experimental analysis and verification[J]. Journal of Mechanical Engineering, 2020, 56(22):148-158.
[10] 韩健,肖新标,杨刚,等.地铁列车-嵌入式轨道系统动力学性能II:轨道参数对动力学性能影响[J].机械工程学报, 2020, 56(24):173-180. HAN Jian, XIAO Xinbiao, YANG Gang, et al. Study on dynamic behaviour of metro train and embedded track system II:effect of track parameters on dynamic behaviour[J]. Journal of Mechanical Engineering, 2020, 56(24):173-180.
[11] 韩健,肖新标,温泽峰,等.地铁列车-嵌入式轨道系统动力学性能研究III:嵌入式轨道与普通轨道动态响应对比分析[J].机械工程学报, 2022, 58(6):169-176. HAN Jian, XIAO Xinbiao, WEN Zefeng, et al. Study on dynamic behaviour of metro train and embedded track system III:dynamic response comparative analysis of embedded track and common track[J]. Journal of Mechanical Engineering, 2022, 58(6):169-176.
[12] HUI C K, NG C F. The effects of floating slab bending resonances on the vibration isolation of rail viaduct[J]. Applied Acoustics, 2009, 70(6):830-844.
[13] 丁德云,刘维宁,张宝才,等.浮置板轨道的模态分析[J].铁道学报, 2008, 30(3):61-64. DING Deyun,LIU Weining,ZHANG Baocai,et al. Modal analysis on the floating slab track[J]. Journal of the China Railway Society, 2008, 30(3):61-64.
[14] 韦凯,豆银铃,赵东锋,等.磁流变阻尼半主动隔振的钢弹簧浮置板轨道动力响应分析[J].中南大学学报, 2018, 49(6):1566-1572. WEI Kai, DOU Yinling, ZHAO Dongfeng, et al. Vibration response analysis of spring-steel floating slab track with semi-active vibration-isolation magneto-rheological dampers[J]. Journal of Central South University, 2018, 49(6):1566-1572.
[15] ZHAO Zeming, WEI Kai, REN Juanjuan, et al. Vibration response analysis of floating slab track supported by nonlinear quasi-zero-stiffness vibration isolators[J]. Journal of Zhejiang University-Science A, 2021, 22(1):37-52.
[16] WANG Liuchong, ZHAO Yannan, SANG Tao, et al. Ultra-low frequency vibration control of urban rail transit:the general quasi-zero-stiffness vibration isolator[J]. Vehicle System Dynamics, 2021, 60(5):1788-1805..
[17] WEI Kai, ZHAO Zeming, DU Xianggang, et al. A theoretical study on the train-induced vibrations of a semi-active magnetorheological steel-spring floating slab track[J]. Construction and Building Materials, 2019, 204:703-715.
[18] 刘韦,朱光楠,杜香刚,等.具有高静低动刚度特性的浮置板隔振器设计方法研究[J].振动与冲击, 2022, 41(15):1-10, 19. LIU Wei, ZHU Guangnan, DU Xianggang, et.al. Study on design method of floating slab vibration isolator with high static and low dynamic stiffness characteristic[J]. Journal of Vibration and Shock, 2022, 41(15):1-10, 19.
[19] 温激鸿,郁殿龙,王刚,等.周期结构细直梁弯曲振动中的振动带隙[J].机械工程学报, 2005, 41(4):1-6. WEN Jihong, YU Dianlong, WANG Gang, et al. Elastic wave band gaps in flexural vibration of straight beams[J]. Journal of Mechanical Engineering, 2005, 41(4):1-6.
[20] RIVA E, RONEO M D, ELAB A, et al. Non-reciprocal wave propagation in discretely modulated spatiotemporal plates[J]. Journal of Sound and Vibration, 2020, 471, 115186.
[21] 朱晓辉,李隆球,张广玉,等.基于层状周期性结构的声波调控技术研究[J].机械工程学报, 2017, 53(6):10-15 ZHU Xiaohui, LI Longqiu, ZHANG Guangyu, et.al. Investigation of acoustic manipulation by layered periodic composites[J]. Journal of Mechanical Engineering, 2017, 53(6):10-15.
[22] WANG Chuanlong, YAO Xiongliang, WU Guoxun, et al. Complete vibration band gap characteristics of two-dimensional periodic grid structures[J]. Composite Structures, 2021, 274, 114368.
[23] ZHANG Peng, WEI Peijun, LI Yueqiu. The elastic wave propagation through the finite and infinite periodic laminated structure of micropolar elasticity[J]. Composite Structures, 2018, 200:358-370.
[24] 冯青松,杨舟,郭文杰,等.周期离散支承钢轨垂向振动带隙特性分析[J].中国科学:技术科学, 2020, 50:1563-1576. FENG Qingsong, YANG Zhou, GUO Wenjie, et al. Analysis of vertical vibration band gap characteristics of periodic discrete support rail[J]. Sci Sin Tech, 2020, 50:1563-1576.
[25] WANG Ping, YI Qiang, ZHAO Caiyou, et al. Elastic wave propagation characteristics of periodic track structure in high-speed railway[J]. Journal of Vibration and Control, 2019, 25(3):517-528.
[26] 易强,王平,赵才友,等.有砟轨道结构弹性波传播特性研究[J].铁道学报, 2019, 41(6):137-145. YI Qiang, WANG Ping, ZHAO Caiyou, et al. Study on elastic wave propagation properties of ballast track structure[J]. Journal of The China Railway Society, 2019, 41(6):137-145.
[27] 冯青松,廖宝亮,郭文杰,等.基于能量泛函变分原理的三层有砟轨道垂向振动带隙分析[J].铁道学报, 2022, 44(4):96-103. FENG Qingsong, LIAO Baoliang, GUO Wenjie, et al. Band-gap analysis of vertical vibration of three-layer ballast track structure based on energy functional variational principle[J]. Journal of The China Railway Society, 2022, 44(4):96-103.
[28] 冯青松,杨舟,郭文杰,等.基于人工弹簧模型的周期结构带隙计算方法研究[J].力学学报, 2021, 53(6):1684-1697. FENG Qingsong, YANG Zhou, GUO Wenjie, et al. Research on band gap calculation method of periodic structure based on artificial spring model[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6):1684-1697.
[29] FENG Qingsong, DAI Chengxin, GUO Wenjie, et al. A Hybrid solution for band-gap analysis of vertical vibration for periodic beam-plate coupled systems based on variation principle[J]. International Journal of Structural Stability and Dynamics, 2021, 21(12), 2150173.
[30] 易强,王平,王树国,等.周期性三维轨道结构弹性波耦合与转换[J].铁道学报, 2022, 44(1):86-95. YI Qiang, WANG Ping, WANG Shuguo, et al. Coupling and conversion of elastic waves in periodic three-dimensional track structure[J]. Journal of The China Railway Society, 2022, 44(1):86-95.
[31] 冯青松,戴承欣,郭文杰,等.周期性钢弹簧浮置板轨道垂向振动带隙特性研究[J].中国铁道科学, 2022, 43(1):17-28. FENG Qingsong, DAI Chengxin, GUO Wenjie, et al. Study on vertical vibration band gap properties of periodic steel spring floating slab track[J]. China Railway Science, 2022, 43(1):17-28.
[32] ZHAO Caiyou, ZHENG Junyuan, SANG Tao, et al. Computational analysis of phononic crystal vibration isolators via FEM coupled with the acoustic black hole effect to attenuate railway-induced vibration[J]. Journal of Vibration and Control, 2019, 25(3):517-528.
[33] 盛曦,曾会柯,石灿,等.声子晶体型浮置板轨道低频减振性能研究[J].振动与冲击, 2022, 41(12):36-42, 107. SHENG Xi, ZENG Huike, SHI Can, et al. A study on low-frequency vibration-mitigation performance of a phononic crystal floating slab track[J]. Journal of Vibration and Shock, 2022, 41(12), 36-42, 107.
[34] 盛曦,曾会柯,石灿,等. TID隔振器浮置板轨道低频减振特性研究[J].工程力学, 2023, 40(5):49-58. SHENG Xi, ZENG Huike, SHI Can, et al. Study on low-frequency vibration mitigation characteristics of TID-vibration-isolator floating slab track[J]. Engineering Mechanics, 2022, 39, 40(5):49-58.
[35] FENG Qingsong, YANG Zhou, GUO Wenjie, et al. Enhanced suppression of vibrational wave transmission in structures with periodically attached absorbers exploiting amplitude magnification mechanisms[J]. European Journal of Mechanics/A Solids, 2022, 95:104666.
[36] DENG Jie, GUASCH O, ZHENG Ling. Reconstructed Gaussian basis to characterize flexural wave collimation in plates with periodic arrays of annular acoustic black holes[J]. International Journal of Mechanical Sciences, 2020, 194, 106179.
[37] WU T X, THOMPSON D J. Vibration analysis of railway track with multiple wheels on the rail[J]. Journal of Sound and Vibration, 2001, 239(1):69-91.
[38] 王党雄,李小珍,张迅,等.轨道结构形式对箱梁中高频振动的影响研究[J].土木工程学报, 2017, 50(8):68-77. WANG Dangxiong, LI Xiaozhen, ZHANG Xun, et. al. Study on the influences of different tracks on the medium-and high-frequency vibrations of a box girder[J]. China Civil Engineering Journal, 2017, 50(8):68-77.
[39] 雷晓燕,张斌,刘庆杰.轨道过渡段动力特性的有限元分析[J].中国铁道科学, 2009, 30(5):15-21. LEI Xiaoyan, ZHANG Bin, LIU Qingjie. Finite element analysis on the dynamic characteristics of the track transition[J]. China Railway Science, 2009, 30(5):15-21.
[40] 韦凯,杨帆,王平,等.扣件胶垫刚度的频变性对地铁隧道环境振动的影响[J].铁道学报, 2015, 37(4):80-86. WEI Kai, YANG Fan, WANG Ping, et al. Influence of frequency-dependent stiffness of rail pads on environment vibration induced by subway in tunnel[J]. Journal of the China Railway Society, 2015, 37(4):80-86.