Investigation of maximum vertical free vibration response of a bridge based on moving load spectrum
LI Jinhua1,2, ZHANG Yao2， ZHANG Huantao2， LAN Shengning3
1.Department of Civil Engineering, East China Jiaotong University, Nanchang 330013, China; 2.National Experimental Teaching Demonstration of Civil Engineering, East China Jiaotong University, Nanchang 330013, China; 3.Department of Civil Engineering, Beibu Gulf University, Qinzhou 535011, China
A frequency domain analysis method based on moving load spectrum was presented for investigating the maximum free vibration response of a bridge.In frequency domain, the Fourier transform was used to obtain the moving load spectrum and the vibration displacement response spectrum of the bridge subjected to moving loads.Corresponding to the maximum value of the moving load amplitude spectrum, the relationship between the dimensionless speed and the axle-span ratio (the ratio of the load wheelbase to the bridge span) was established by the combined use of theoretical derivation and numerical analysis.Then according to the relationship, the speed expression of the maximum free vibration displacement response of the bridge under moving loads was proposed, it is obviously different from the resonance speed.Finally, taking two simply supported girder bridges with different spans as examples, the maximum displacement free vibration response of the bridges was calculated with different ratio of axle span to moving load speed in time-domain, in order to verify the correctness of the results of the frequency domain analysis.The results show that the maximum free vibration response of the bridge can be effectively reflected by moving load spectrum; when the axle-span ratio is 0.72, the maximum response of the bridge is the smallest; when the axle-span ratio is 0 or 1.47, the maximum response of the bridge is the largest; when the moving load travels at the speed according to the speed expression mentioned above, the maximum displacement free vibration response of the bridge will be generated.
李锦华，张耀，张焕涛，蓝声宁. 基于移动荷载谱的桥梁竖向自由振动最大响应研究[J]. 振动与冲击, 2021, 40(14): 261-267.
LI Jinhua, ZHANG Yao， ZHANG Huantao， LAN Shengning. Investigation of maximum vertical free vibration response of a bridge based on moving load spectrum. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(14): 261-267.
［1］王少钦, 马骎, 夏禾, 等.风-列车-大跨度悬索桥系统非线性耦合振动分析［J］.工程力学, 2016, 33(12):150-157.
WANG Shaoqin, MA Qin, XIA He, et al.Nonlinear dynamic analysis of a wind-train-long-span suspension bridge coupling system［J］.Engineering Mechanics, 2016, 33(12):150-157.
［2］吕龙, 李建中.列车制动和运行下大跨度公铁两用斜拉桥纵向振动分析［J］.铁道学报, 2017, 39(3):90-95.
L Long, LI Jianzhong.Study on longitudinal vibration of long-span rail-cum-road cable-stayed bridge induced by train braking and running［J］.Journal of the China Railway Society, 2017, 39(3):90-95.
［3］YANG Y B, YAU J D.Resonance of high-speed trains moving over a series of simple or continuous beams with non-ballasted tracks［J］.Engineering Structures,2017,143:295-305.
［4］GRECO F, LONETTI P.Numerical formulation based on moving mesh method for vehicle-bridge interaction［J］.Advances in Engineering Software, 2018, 121:75-83.
［5］晋智斌, 李小珍, 朱艳,等.列车-桥梁耦合系统非线性随机振动分析［J］.铁道学报, 2017(9):114-121.
JIN Zhibin, LI Xiaozhen, ZHU Yan, et al.Random vibration analysis of nonlinear vehicle-bridge dynamic interactions［J］.Journal of the China Railway Society, 2017(9):114-121.
［6］黄文杰, 罗光财, 彭丹, 等.高速铁路简支梁桥参数变化对竖向共振影响分析［J］.铁道科学与工程学报, 2016, 13(8):1474-1481.
HUANG Wenjie, LUO Guangcai, PENG Dan, et al.Analysis of the influence of parameter variation of vertical beam bridge on vertical resonance of high-speed railway［J］.Journal of Railway Science and Engineering, 2016, 13(8): 1474-1481.
［7］YAU J D.Resonance of continuous bridges due to high speed trains［J］.Journal of Marine Science and Technology, 2001, 9(1):14-20.
［8］WANG Y J, WEI Q C, YAU J D.Interaction response of train loads moving over a two-span continuous beam ［J］.International Journal of Structural Stability and Dynamics, 2013, 13(1):1350002.
［9］吕龙, 李建中.移动荷载作用下大跨度铁路斜拉桥纵向共振机理［J］.土木工程学报, 2018(2):81-87.
L Long, LI Jianzhong.Longitudinal resonance mechanism of long-span railway cable-stayed bridge under moving loads［J］.China Civil Engineering Journal, 2018(2): 81-87.
［10］YANG Y B, LIN C L, YAU J D, et al.Mechanism of resonance and cancellation for train-induced vibrations on bridges with elastic bearings［J］.Journal of Sound and Vibration, 2004, 269(1):345-360.
［11］李慧乐, 夏禾, 郭薇薇.简支梁在列车荷载下的共振与消振效应［J］.振动工程学报, 2014, 27(2):172-179.
LI Huile, XIA He, GUO Weiwei.Resonance and vibration absorbing effect of simply supported beam under train load［J］.Journal of Vibration Engineering,2014,27(2):172-179.
［12］李慧乐, 夏禾, 郭薇薇.移动荷载作用下简支梁共振与消振机理研究［J］.工程力学, 2013, 30(7):47-54.
LI Huile, XIA He, GUO Weiwei.Study on mechanism of resonance and vibration cancellation for simply-supported beam under moving load［J］.Engineering Mechaanics, 2013, 30(7): 47-54.
［13］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.
［14］PESTEREV A V, YANG B, BERGMAN L A, et al.Revisiting the moving force problem［J］.Journal of Sound and Vibration, 2003, 261(1):75-91.
［15］MUSEROS P, MOLINER E, MARTINEZ-RODRIGO M D.Free vibrations of simply-supported beam bridges under moving loads: maximum resonance, cancellation and resonant vertical acceleration［J］.Journal of Sound and Vibration, 2013, 332(2):326-345.
［16］夏禾, 张楠楠, 郭薇薇.车桥耦合振动工程［M］.北京: 科学出版社,2014.
［17］YANG Y B, YAU J D, WU Y S.Vehicle-bridge interaction dynamics［M］∥Vehicle-bridge Interaction Dynamics with Applications to High-speed Railways.Singapore:World Scientific, 2004.
