기존선 철도차량을 이용한 철도교의 상호작용해석

조은상(Cho Eun Sang),김희주(Kim Hee Ju),황원섭(Hwang Won Sup) 대한토목학회 2009 대한토목학회논문집 A Vol.29 No.1A

In this study, the numerical method is presented, which can consider the various train types and can solve the equations of motion for a vehicle-bridge interaction analysis by non-iteration procedure through formulating the coupled equations of motion. The coupled equations of motion for the vehicle-bridge interaction are solved by the Newmark β of a direct integration method, and by composing the effective stiffness matrix and the effective force vector according to a analysis step, those can be solved with the same manner of the solving procedure of equilibrium equations in static analysis. Also, the effective stiffness matrix is reconstructed by the Skyline method for increasing the analysis effectiveness. The Cholesky's matrix decomposition scheme is applied to the analysis procedure for minimizing the numerical errors that can be generated in directly calculating the inverse matrix. The equations of motion for the conventional trains are derived, and the numerical models of the conventional trains are idealized by a set of linear springs and dashpots with 16 degrees of freedom. The bridge models are simplified by the 3 dimensional space frame element which is based on the Euler-Bernoulli theory. The rail irregularities of vertical and lateral directions are generated by the PSD functions of the Federal Railroad Administration (FRA). The results of the vehicle-bridge interaction analysis are verified by the experimental results for the railway plate girder bridges of a span length with 12 m, 18 m, and the experimental and analytical data are applied to the low pass filtering scheme, and the basis frequency of the filtering is a 2 times of the 1st fundamental frequency of a bridge bending. 본 논문에서는 다양한 차종의 영향을 반영할 수 있고, 차량과 교량의 연성 운동방정식을 구성하여 시간 단계별 직접해를 산정할 수 있는 수치해석기법을 제시하였다. 운동방정식의 해는 직접적분법인 Newmark β을 이용하여 해석 단계별로 구성된 유효강성행렬과 유효하중벡터를 바탕으로 정적평형방정식의 해를 구하는 원리와 동일하게 산정하였다. 또한 해석의 효율성을 증진시키기 위하여 유효강성행렬은 Skyline 법에 의해 재구성하였으며. Cholesky의 행렬 분해기법을 동시에 적용하여 직접적인 역행렬 계산에서 야기되는 오차의 발생을 최소화 하였다. 또한 기존선 철도차량인 새마을 PMC 열차와 디젤 견인 무궁화 열차에 대한 3차원 정밀수치해석 모델을 개발하였고, 각 차량은 차체와 전ㆍ후방 대차에 각각 6자유도씩 고려하여 총 18자유도로 수치모델을 작성하였다. 교량은 3차원 공간뼈대 요소를 이용하여 모델링하였고, 차륜과 레일 접촉면의 불규칙성은 미국의 FRA에서 규정하고 있는 연직방향 및 횡방향틀림에 대한 PSD 함수를 이용하여 궤도틀림을 수치적으로 구현하였다. 제시된 수치해석 기법은 12 m, 18 m형 판형교의 실측결과를 이용하여 타당성을 검증하였으며, 실측 및 수치해석결과는 교량의 1차 휨 고유진동수의 2.0배를 기준으로 Low pass filtering 하였다.

Variability in bridge frequency induced by a parked vehicle

Chang, K.C.,Kim, C.W.,Borjigin, Sudanna Techno-Press 2014 Smart Structures and Systems, An International Jou Vol.13 No.5

The natural frequency of a bridge is an important parameter in many engineering applications such as bridge seismic design and modal-based bridge health monitoring. The natural frequency of a bridge vibrating alone may differ from that vibrating along with a vehicle. Although such vehicle-induced variability in bridge frequency is revealed in several experimental and numerical simulation studies, few attempts have been made on the theoretical descriptions. In this study, both theoretically and experimentally, the variability in the bridge frequency induced by a parked vehicle is verified, and is therefore suggested to be considered in bridge-related engineering, especially for those cases with near vehicle-bridge resonance conditions or with large vehicle-to-bridge mass ratios. Moreover, the variability ranges could be estimated by an analytical formula presented herein.

Finite element analysis of vehicle-bridge interaction by an iterative method

Jo, Ji-Seong,Jung, Hyung-Jo,Kim, Hongjin Techno-Press 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.30 No.2

In this paper, a new iterative method for solving vehicle-bridge interaction problems is proposed. Iterative methods have advantages over the non-iterative methods in that it is not necessary to update the system matrix for a given wheel location, and the method can be applied for a new type of car or bridge with few or no modifications. In the proposed method, the necessity of system matrices update is eliminated using the equivalent interaction force acting on the bridge, which is obtained iteratively. Ballast stiffness is included in the interaction forces and the geometric compatibility at the contact points are used as convergence criteria. The bridge is considered as an elastic Bernoulli-Euler beam with surface irregularity and ballast stiffness. The moving vehicle is modeled as a multi-axle mass-spring-damper system having many degrees of freedom depending on the number of axles. The pitching effect, which is the interaction effect between the rear and front wheels when a vehicle begins to enter or leave the bridge, is also considered in the formulation including extended ground boundaries having surface irregularity and ballast stiffness. The applicability of the proposed method is illustrated in the numerical studies.

Effect of road surface roughness on the response of a moving vehicle for identification of bridge frequencies

Yang, Y.B.,Li, Y.C.,Chang, K.C. Techno-Press 2012 Interaction and multiscale mechanics Vol.5 No.4

Measuring the bridge frequencies indirectly from an instrumented test vehicle is a potentially powerful technique for its mobility and economy, compared with the conventional direct technique that requires vibration sensors to be installed on the bridge. However, road surface roughness may pollute the vehicle spectrum and render the bridge frequencies unidentifiable. The objective of this paper is to study such an effect. First, a numerical simulation is conducted using the vehicle-bridge interaction element to demonstrate how the surface roughness affects the vehicle response. Then, an approximate theory in closed form is presented, for physically interpreting the role and range of influence of surface roughness on the identification of bridge frequencies. The latter is then expanded to include the action of an accompanying vehicle. Finally, measures are proposed for reducing the roughness effect, while enhancing the identifiability of bridge frequencies from the passing vehicle response.

Variability in bridge frequency induced by a parked vehicle

K.C. Chang,C.W. Kim,Sudanna Borjigin 국제구조공학회 2014 Smart Structures and Systems, An International Jou Vol.13 No.5

The natural frequency of a bridge is an important parameter in many engineering applications such as bridge seismic design and modal-based bridge health monitoring. The natural frequency of a bridge vibrating alone may differ from that vibrating along with a vehicle. Although such vehicle-induced variability in bridge frequency is revealed in several experimental and numerical simulation studies, few attempts have been made on the theoretical escriptions. In this study, both theoretically and experimentally, the variability in the bridge frequency induced by a parked vehicle is verified, and is therefore suggested to be considered in bridge-related engineering, especially for those cases with near vehicle-bridge resonance conditions or with large vehicle-to-bridge mass ratios. Moreover, the variability ranges could be estimated by an analytical formula presented herein.

Random Vibration Analysis of a Vehicle–Bridge Interaction System Subjected to Traveling Seismic Ground Motions Using Pseudo-excitation Method

MACHUNYAN,최동호 한국강구조학회 2022 International Journal of Steel Structures Vol.22 No.6

For long, multi-span bridges, traveling seismic waves arrive at diff erent bridge support points at diff erent times. To study this diff erence, random dynamic vibration analysis of a vehicle–bridge interaction system under traveling seismic ground motions was performed in the present paper. A vehicle model with 27 degrees of freedom is used, while three-dimensional Euler beams are used to model the track and the bridge. The equation of motion of the vehicle–bridge interaction system was established through the wheel-rail relationship. The expression of the standard deviation of the system vibrations and the running safety factor is derived by the pseudo-excitation method. The proposed method is validated by comparing random bridge vibrations using the Monte-Carlo method. As a case study, a Chinese-made electric multiple unit train running on a ten-span simply supported bridge is analyzed under track irregularities and seismic ground motions with consideration of the eff ects of diff erent train speeds, diff erent seismic intensities, and diff erent seismic wave propagation velocities. The results show that wave propagation velocities signifi cantly aff ect the random vibration performances and the running safety of the vehicle-bridge interaction system. Therefore, it is important to include wave propagation velocities when calculating the random seismic vibrations of a vehicle-bridge interaction system.

Finite element analysis of vehicle-bridge interaction by an iterative method

Ji-Seong Jo,정형조,Hongjin Kim 국제구조공학회 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.30 No.2

In this paper, a new iterative method for solving vehicle-bridge interaction problems is proposed. Iterative methods have advantages over the non-iterative methods in that it is not necessary to update the system matrix for a given wheel location, and the method can be applied for a new type of car or bridge with few or no modifications. In the proposed method, the necessity of system matrices update is eliminated using the equivalent interaction force acting on the bridge, which is obtained iteratively. Ballast stiffness is included in the interaction forces and the geometric compatibility at the contact points are used as convergence criteria. The bridge is considered as an elastic Bernoulli-Euler beam with surface irregularity and ballast stiffness. The moving vehicle is modeled as a multi-axle mass-spring-damper system having many degrees of freedom depending on the number of axles. The pitching effect, which is the interaction effect between the rear and front wheels when a vehicle begins to enter or leave the bridge, is also considered in the formulation including extended ground boundaries having surface irregularity and ballast stiffness. The applicability of the proposed method is illustrated in the numerical studies.

A drive-by inspection system via vehicle moving force identification

P.J. McGetrick,E.J. OBrien,A. González 국제구조공학회 2014 Smart Structures and Systems, An International Jou Vol.13 No.5

This paper presents a novel method to carry out monitoring of transport infrastructure such as pavements and bridges through the analysis of vehicle accelerations. An algorithm is developed for the identification of dynamic vehicle-bridge interaction forces using the vehicle response. Moving force identification theory is applied to a vehicle model in order to identify these dynamic forces between the vehicle and the road and/or bridge. A coupled half-car vehicle-bridge interaction model is used in theoretical simulations to test the effectiveness of the approach in identifying the forces. The potential of the method to identify the global bending stiffness of the bridge and to predict the pavement roughness is presented. The method is tested for a range of bridge spans using theoretical simulations and the influences of road roughness and signal noise on the accuracy of the results are investigated.

A drive-by inspection system via vehicle moving force identification

OBrien, E.J.,McGetrick, P.J.,Gonzalez, A. Techno-Press 2014 Smart Structures and Systems, An International Jou Vol.13 No.5

This paper presents a novel method to carry out monitoring of transport infrastructure such as pavements and bridges through the analysis of vehicle accelerations. An algorithm is developed for the identification of dynamic vehicle-bridge interaction forces using the vehicle response. Moving force identification theory is applied to a vehicle model in order to identify these dynamic forces between the vehicle and the road and/or bridge. A coupled half-car vehicle-bridge interaction model is used in theoretical simulations to test the effectiveness of the approach in identifying the forces. The potential of the method to identify the global bending stiffness of the bridge and to predict the pavement roughness is presented. The method is tested for a range of bridge spans using theoretical simulations and the influences of road roughness and signal noise on the accuracy of the results are investigated.

Analysis of high-speed vehicle-bridge interactions by a simplified 3-D model

Song, Myung-Kwan,Choi, Chang-Koon Techno-Press 2002 Structural Engineering and Mechanics, An Int'l Jou Vol.13 No.5

In this study, the analysis of high-speed vehicle-bridge interactions by a simplified 3-dimensional finite element model is performed. Since railroads are constructed mostly as double tracks, there exists eccentricity between the vehicle axle and the neutral axis of cross section of a railway bridge. Therefore, for the more efficient and accurate vehicle-bridge interaction analysis, the analysis model should include the eccentricity of axle loads and the effect of torsional forces acting on the bridge. The investigation into the influences of eccentricity of the vehicle axle loads and vehicle speed on vehicle-bridge interactions are carried out for two cases. In the first case, only one train moves on its track and in the other case, two trains move respectively on their tracks in the opposite direction. From the analysis results of an existing bridge, the efficiency and capability of the simplified 3-dimensional model for practical application can be also verified.