移动简谐荷载作用下轨道结构动态响应研究
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摘要
研究了移动简谐荷载作用下轨道结构的动态响应特性,首先,将轨道结构简化为连续离散点支撑的弹性Euler梁模型,并建立了移动荷载作用下轨道系统动力学微分方程,基于无限周期结构在频域内的性质和叠加原理,推导出了移动简谐荷载作用下轨道结构上任意点的动态响应解析表达式;然后,数值分析了激励频率、扣件刚度、扣件阻尼对轨道结构动态响应的影响。研究结果表明:钢轨动态响应共振峰出现在荷载激励频率附近;随着激励频率的增大,钢轨动态响应峰值向高频方向移动;在高频段内,钢轨动态响应随着扣件刚度的增大而增大;扣件阻尼对系统的共振峰值及峰值带宽无显著影响,但在高频段内扣件阻尼具有明显抑制振动的作用,通过增大阻尼可以有效控制轨道的高频振动。
The dynamic response characteristics of the track structure under moving harmonic load are investigated. Firstly, the track is simplified as an Euler beam model periodically supported by continuous discrete point, the dynamic differential equation of vertical vibration for the track structure is formulated. Based on the dynamic response characteristics of the periodic structure under a moving harmonic load in frequency domain and the superposition principle, the analytical expression for the dynamic response of any point on the track structure under moving harmonic load is derived consequently. The influences of excitation frequency, fasteners stiffness and fasteners damping on the dynamic response of the track structure are numerically analyzed in detail. The results indicate that the response peaks of the track structure occur in the vicinity of the exciting frequency, and the dynamic response decreases rapidly at the area away from exciting frequency. The response peak will move towards higher frequency with the increase of excitation frequency. In high frequency band, the increase of fasteners stiffness will lead to the improvement of the dynamic response. The changes of the fasteners damping have no significant effects on the resonant peak and the peak bandwidth of the system, however the fasteners damping plays a significant role on restraining the vibration in high frequency band. Therefore, the strong vibration of the track structure can be effectively controlled by increasing the damping.
The dynamic response characteristics of the track structure under moving harmonic load are investigated. Firstly, the track is simplified as an Euler beam model periodically supported by continuous discrete point, the dynamic differential equation of vertical vibration for the track structure is formulated. Based on the dynamic response characteristics of the periodic structure under a moving harmonic load in frequency domain and the superposition principle, the analytical expression for the dynamic response of any point on the track structure under moving harmonic load is derived consequently. The influences of excitation frequency, fasteners stiffness and fasteners damping on the dynamic response of the track structure are numerically analyzed in detail. The results indicate that the response peaks of the track structure occur in the vicinity of the exciting frequency, and the dynamic response decreases rapidly at the area away from exciting frequency. The response peak will move towards higher frequency with the increase of excitation frequency. In high frequency band, the increase of fasteners stiffness will lead to the improvement of the dynamic response. The changes of the fasteners damping have no significant effects on the resonant peak and the peak bandwidth of the system, however the fasteners damping plays a significant role on restraining the vibration in high frequency band. Therefore, the strong vibration of the track structure can be effectively controlled by increasing the damping.
引文
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[17]SHI L,CAI Y,WANG P,et al.A theoretical investigation on influences of slab tracks on vertical dynamic responses of railway viaducts[J].Journal of sound&vibration,2016,374:138-154.
[2]张铎,李小珍.移动简谐荷载列作用下简支梁竖向动力响应的解析解及其应用研究[J].应用力学学报,2014,31(1):144-149.(ZHANG Duo,LI Xiaozhen.Analysis and application of vertical dynamic response of simply supported beam bridge under moving harmonic load series[J].Chinese journal of applied mechanics,2014,31(1):144-149(in Chinese)).
[3]LIU W N,ZHANG Y Q.Periodic analytical solution of railway track structure under moving loads[J].Engineering mechanics,2004,21(5):90-100.
[4]李小珍,张志俊,刘全民.任意移动荷载列作用下简支梁桥竖向振动响应解析分析[J].振动与冲击,2012,31(20):137-142.(LIXiaozhen,ZHANG Zhijun,LIU Quanmin.Vertical dynamic response analysis of a simply supported beam bridge under successive moving loads[J].Journal of vibration and shock,2012,31(20):137-142(in Chinese)).
[5]李克飞,刘维宁,贾颖绚.变速移动荷载下轨道结构动力响应解析解研究[J].工程力学,2011,28(9):207-213.(LI Kefei,LIUWeining,JIA Yingxuan.An analytical solution for railway track structure response under moving loads with variable speeds[J].Engineering mechanics,2011,28(9):207-213(in Chinese)).
[6]SUN W,ZHOU J,THOMPSON D,et al.Vertical random vibration analysis of vehicle-track coupled system using Green's function method[J].Vehicle system dynamics,2014,52(3):362-389.
[7]BELOTSERKOVSKIY P M.On the oscillations of infinite periodic beams subjected to a moving concentrated force[J].Journal of sound and vibration,1996,193(3):705-712.
[8]雷晓燕.轨道结构动力分析的傅里叶变换法[J].铁道学报,2007,29(3):67-71.(LEI Xiaoyan.Dynamic analyses of track structure with Fourier transform technique[J].Journal of the China railway society,2007,29(3):67-71(in Chinese)).
[9]MA L X,LIU W N,LI K F.Fast numerical algorithm of floating slab track vibration response under moving loads in the frequency domain[J].Journal of the China railway society,2014,36(2):86-94.
[10]刘维宁,张昀青.轨道结构在移动荷载作用下的周期解析解[J].工程力学,2004,21(5):100-102.(LIU Weining,ZHANG Yunqing.Aperiodic analytical solution of railway track structure under moving loads[J].Engineering mechanics,2004,21(5):100-102(in Chinese)).
[11]SHENG X,JONES C J C,THOMPSON D J.Responses of infinite periodic structures to moving or stationary harmonic loads[J].Journal of sound&vibration,2005,282(1/2):125-149.
[12]SHENG X,ZHONG T,LI Y.Vibration and sound radiation of slab high-speed railway tracks subject to a moving harmonic load[J].Journal of sound&vibration,2017,395:160-186.
[13]马龙祥,刘维宁,刘卫丰.移动荷载作用下周期支撑轨道结构振动研究[J].中国铁道科学,2013,34(1):1-7.(MA Longxiang,LIU Weining,LIU Weifeng.Study on vibration of periodic supported track structure under moving loads[J].China railway science,2013,34(1):1-7(in Chinese)).
[14]NORDBORG A.Vertical rail vibration:point force excitation[J].Acta acustica united with acustica,1998,84(2):280-288.
[15]李克飞,刘维宁,吴宗臻.变速移动质量作用下轨道动力响应解析解研究[J].工程力学,2014,31(7):162-169.(LI Kefei,LIUWeining,WU Zongzhen.Analytical study on the vibration response of the track subjected to the moving mass with variable speeds[J].Engineering mechanics,2014,31(7):162-169(in Chinese)).
[16]CAI Y,CAO Z,SUN H,et al.Effects of the dynamic wheel-rail interaction on the ground vibration generated by a moving train[J].International journal of solids&structures,2010,47(17):2246-2259.
[17]SHI L,CAI Y,WANG P,et al.A theoretical investigation on influences of slab tracks on vertical dynamic responses of railway viaducts[J].Journal of sound&vibration,2016,374:138-154.