Vehicle Scanning Method for Bridges

YEONG-BIN YANG, PHD, is Honorary Dean of Civil Engineering, Chongqing University in China, Feng Tay Chair Professor of National Yunlin University of Science and Technology (YunTech), and Professor Emeritus of National Taiwan University (NTU) in Taiwan. He is a member of the Chinese Academy of Engineering, Austrian Academy of Sciences, and EU Academy of Sciences. Also, he is an Editor-in-Chief of the International Journal of Structural Stability and Dynamics, President of the Asian-Pacific Association of Computational Mechanics (APACM), and Chairman of the East Asia-Pacific Conference on Structural Engineering and Construction (EASEC). JUDY P. YANG, PHD, is an Associate Professor in the Dept. of Civil Engineering, National Chiao Tung University, Taiwan. BIN ZHANG is a PhD student in the School of Civil Engineering, Chongqing University in China. YUNTIAN WU, PHD, is a Professor in the School of Civil Engineering, Chongqing University, China.

• Preface ixAcknowledgments xiii1 Introduction 11.1 Modal Properties of Bridges 11.2 Basic Concept of the Vehicle Scanning Method 31.2.1 Bridge Frequency Extraction 31.2.2 Bridge Mode Shapes Construction 41.3 Brief on the Works Conducted by Yang and Co‐Workers 51.4 Works Done by Researchers Worldwide 71.4.1 Theoretical Analysis and Simulation 81.4.2 Laboratory Test 161.4.3 Field Investigation 201.5 Concluding Remarks 222 Vehicle Scanning of Bridge Frequencies: Simple Theory 252.1 Introduction 252.2 Formulation of the Analytical Theory 272.3 Single‐ Mode Analytical Solution 282.4 Condition of Resonance 342.5 Simulation by the Finite Element Method (FEM) 392.6 Verification of Accuracy of Analytical Solutions 412.7 Extraction of Fundamental Frequency of Bridge 422.7.1 Effect of Moving Speed of the Vehicle 462.7.2 Condition of Resonance 462.7.3 Effect of Damping of the Bridge 482.7.4 Effect of a Vehicle Traveling over a Stiffer Bridge 492.8 Concluding Remarks 503 Vehicle Scanning of Bridge Frequencies: General Theory 513.1 Introduction 513.2 Physical Modeling and Formulation 533.3 Dynamic Response of the Beam 553.3.1 Beam’s Response to a Single Moving Vehicle 583.3.2 Beam’s Response to Five Moving Vehicles 613.4 Dynamic Response of the Moving Vehicle 623.5 Numerical Verification 663.6 Concluding Remarks 694 Vehicle Scanning of Bridge Frequencies: Experiment 714.1 Introduction 714.2 Objective of This Chapter 724.3 Description of the Test Bridge 734.4 Description of the Test Vehicle 734.5 Instrumentation 754.6 Testing Plan 754.7 Eigenvalue Analysis Results 774.8 Experimental Results 774.8.1 Ambient Vibration Test 774.8.2 Vehicle Characteristics Test 784.8.3 Bridge Response to the Moving Truck 794.8.4 Response of the Test Cart Resting on the Bridge to the Moving Truck 814.8.5 Response of the Moving Test Cart with No Ongoing Traffic 834.8.6 Response of the Moving Test Cart with Ongoing Traffic 854.9 Comparing the Measured Results with Numerical Results 864.10 Concluding Remarks 875 EMD‐Enhanced Vehicle Scanning of Bridge Frequencies 915.1 Introduction 915.2 Analytical Formulation of the Problem 935.3 Finite Element Simulation of the Problem 965.4 Empirical Mode Decomposition 975.5 Extraction of Bridge Frequencies by Numerical Simulation 995.5.1 Example 1: Single Moving Vehicle 1015.5.2 Example 2: Five Sequential Moving Vehicles 1025.5.3 Example 3: Five Random Moving Vehicles 1055.6 Experimental Studies 1055.7 Concluding Remarks 1146 Effect of Road Roughness on Extraction of Bridge Frequencies 1156.1 Introduction 1156.2 Simulation of Roughness Profiles 1166.3 Simulation of Bridges with Rough Surface 1176.4 Effect of Road Roughness on Vehicle Response 1186.4.1 Case 1: Vehicle Frequency Less than Any Bridge Frequencies 1196.4.2 Case 2: Vehicle Frequency Greater than the First Bridge Frequency 1196.5 Vehicle Responses Induced by Separate Excitational Sources 1226.6 Closed‐Form Solution of Vehicle Response Considering Road Roughness 1226.7 Reducing the Impact of Road Roughness by Using Two Connected Vehicles 1276.8 Numerical Studies 1316.8.1 Example 1. Two Identical Vehicles Moving over the Bridge of Class A Roughness 1316.8.2 Example 2. Two Identical Vehicles Moving over the Bridge of Class C Roughness 1316.8.3 Example 3. Two Vehicles of Identical Frequency but Different Properties 1326.8.4 Effect of Vehicle Spacing on Identification of Bridge Frequencies 1336.9 Concluding Remarks 1357 Filtering Technique for Eliminating the Effect of Road Roughness 1377.1 Introduction 1377.2 Numerical Simulations for Vehicle Responses 1387.3 Filtering Techniques 1417.3.1 Band‐Pass Filter (BPF)/Band‐Stop Filter (BSF) 1417.3.2 Singular Spectrum Analysis (SSA) 1427.3.3 Singular Spectrum Analysis with Band‐Pass Filter (SSA‐BPF) 1447.4 Case Studies 1457.4.1 Case 1: Vehicle Frequency Smaller than First Bridge Frequency 1457.4.2 Case 2: Vehicle Frequency Greater than First Bridge Frequency 1487.5 Concluding Remarks 1518 Hand‐Drawn Cart Used to Measure Bridge Frequencies 1538.1 Introduction 1538.2 Dynamic Properties of the Hand‐Drawn Test Cart 1568.3 Basic Dynamic Tests for the Test Cart 1578.4 Field Tests 1628.4.1 Effect of Cart Weight 1638.4.2 Effect of Various Traveling Speeds 1658.4.3 Various Volumes of Existing Traffic Flows 1708.5 Concluding Remarks 1739 Theory for Retrieving Bridge Mode Shapes 1759.1 Introduction 1759.2 Hilbert Transformation 1769.3 Theoretical Formulation 1779.4 Algorithms and Constraints 1819.5 Case Studies 1859.5.1 Test Vehicle Passing through a Bridge with Smooth Road Surface 1869.5.2 Effect of Vehicle Speed 1879.5.3 Test Vehicle Traveling along with Random Traffic 1909.5.4 Effect of Road Surface Roughness 1909.6 Concluding Remarks 19310 Contact‐Point Response for Modal Identification of Bridges 19510.1 Introduction 19510.2 Theoretical Formulation 19710.2.1 Dynamic Response of the Vehicle−Bridge Contact Point 19810.2.2 Dynamic Response of the Moving Vehicle 19910.2.3 Procedure for Calculating the Contact‐Point Response in a Field Test 20110.2.4 Relationship Between the Contact‐Point and Vehicle Responses 20110.3 Finite Element Simulation of VBI Problems 20410.3.1 Brief on VBI Element 20410.3.2 Verification of the Theoretical Solution 20510.4 Retrieval of Bridge Frequencies 20610.5 Retrieval of Bridge Mode Shapes 20810.5.1 Effect of Moving Speed 20910.5.2 Effect of Vehicle Frequency 21010.6 Effect of Road Roughness 21210.6.1 Bridge with Rough Surface Free of Existing Traffic 21210.6.2 Bridge with Rough Surface under Existing Traffic 21410.7 Concluding Remarks 21511 Damage Detection of Bridges Using the Contact‐Point Response 21711.1 Introduction 21711.2 Dynamic Response of the Vehicle‐Bridge System 21911.2.1 Contact‐Point Response: Analytical Solution 22011.2.2 Contact‐Point Response: For Use in Field Test 22011.3 Algorithm for Damage Detection 22111.3.1 Hilbert Transformation 22111.3.2 Strategy for Damage Detection 22111.4 Finite Element Simulation of the Problem 22311.4.1 Damage Element for Beams 22311.4.2 Brief on Vehicle−Bridge Interaction (VBI) Element Used 22411.5 Detection of Damages on a Beam 22511.5.1 Detection of Damage Location on the Beam 22511.5.2 Detection of Damage Severity 22611.5.3 Detection of Multiple Damages 22811.6 Parametric Study 22811.6.1 Effect of Test Vehicle Speed 22911.6.2 Effect of Measurement Noise 22911.6.3 Bridge with Rough Surface Free of Random Traffic 23011.6.4 Bridge with Rough Surface under Random Traffic 23211.7 Concluding Remarks 234Appendix: Finite Element Simulation 237References 247Author Index 259Subject Index 265