Vehicle Scanning Method for Bridges

Presents the first ever guide for vehicle scanning of the dynamic properties of bridges

Written by the leading author on the subject of vehicle scanning method (VSM) for bridges, this book allows engineers to monitor every bridge of concern on a regular and routine basis, for the purpose of maintenance and damage detection. It includes a review of the existing literature on the topic and presents the basic concept of extracting bridge frequencies from a moving test vehicle fitted with vibration sensors. How road surface roughness affects the vehicle scanning method is considered and a finite element simulation is conducted to demonstrate how surface roughness affects the vehicle response. Case studies and experimental results are also included.

Vehicle Scanning Method for Bridges covers an enhanced technique for extracting higher bridge frequencies. It examines the effect of road roughness on extraction of bridge frequencies, and looks at a dual vehicle technique for suppressing the effect of road roughness. A filtering technique for eliminating the effect of road roughness is also presented. In addition, the book covers the identification of bridge mode shapes, contact-point response for modal identification of bridges, and damage detection of bridges—all through the use of a moving test vehicle.

• The first book on vehicle scanning of the dynamic properties of bridges
• Written by the leading author on the subject
• Includes a state-of-the-art review of the existing works on the vehicle scanning method (VSM)
• Presents the basic concepts for extracting bridge frequencies from a moving test vehicle fitted with vibration sensors
• Includes case studies and experimental results 

The first book to fully cover scanning the dynamic properties of bridges with a vehicle, Vehicle Scanning Method for Bridges is an excellent resource for researchers and engineers working in civil engineering, including bridge engineering and structural health monitoring.

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 ix

Acknowledgments xiii

1 Introduction 1

1.1 Modal Properties of Bridges 1

1.2 Basic Concept of the Vehicle Scanning Method 3

1.2.1 Bridge Frequency Extraction 3

1.2.2 Bridge Mode Shapes Construction 4

1.3 Brief on the Works Conducted by Yang and Co‐Workers 5

1.4 Works Done by Researchers Worldwide 7

1.4.1 Theoretical Analysis and Simulation 8

1.4.2 Laboratory Test 16

1.4.3 Field Investigation 20

1.5 Concluding Remarks 22

2 Vehicle Scanning of Bridge Frequencies: Simple Theory 25

2.1 Introduction 25

2.2 Formulation of the Analytical Theory 27

2.3 Single‐ Mode Analytical Solution 28

2.4 Condition of Resonance 34

2.5 Simulation by the Finite Element Method (FEM) 39

2.6 Verification of Accuracy of Analytical Solutions 41

2.7 Extraction of Fundamental Frequency of Bridge 42

2.7.1 Effect of Moving Speed of the Vehicle 46

2.7.2 Condition of Resonance 46

2.7.3 Effect of Damping of the Bridge 48

2.7.4 Effect of a Vehicle Traveling over a Stiffer Bridge 49

2.8 Concluding Remarks 50

3 Vehicle Scanning of Bridge Frequencies: General Theory 51

3.1 Introduction 51

3.2 Physical Modeling and Formulation 53

3.3 Dynamic Response of the Beam 55

3.3.1 Beam’s Response to a Single Moving Vehicle 58

3.3.2 Beam’s Response to Five Moving Vehicles 61

3.4 Dynamic Response of the Moving Vehicle 62

3.5 Numerical Verification 66

3.6 Concluding Remarks 69

4 Vehicle Scanning of Bridge Frequencies: Experiment 71

4.1 Introduction 71

4.2 Objective of This Chapter 72

4.3 Description of the Test Bridge 73

4.4 Description of the Test Vehicle 73

4.5 Instrumentation 75

4.6 Testing Plan 75

4.7 Eigenvalue Analysis Results 77

4.8 Experimental Results 77

4.8.1 Ambient Vibration Test 77

4.8.2 Vehicle Characteristics Test 78

4.8.3 Bridge Response to the Moving Truck 79

4.8.4 Response of the Test Cart Resting on the Bridge to the Moving Truck 81

4.8.5 Response of the Moving Test Cart with No Ongoing Traffic 83

4.8.6 Response of the Moving Test Cart with Ongoing Traffic 85

4.9 Comparing the Measured Results with Numerical Results 86

4.10 Concluding Remarks 87

5 EMD‐Enhanced Vehicle Scanning of Bridge Frequencies 91

5.1 Introduction 91

5.2 Analytical Formulation of the Problem 93

5.3 Finite Element Simulation of the Problem 96

5.4 Empirical Mode Decomposition 97

5.5 Extraction of Bridge Frequencies by Numerical Simulation 99

5.5.1 Example 1: Single Moving Vehicle 101

5.5.2 Example 2: Five Sequential Moving Vehicles 102

5.5.3 Example 3: Five Random Moving Vehicles 105

5.6 Experimental Studies 105

5.7 Concluding Remarks 114

6 Effect of Road Roughness on Extraction of Bridge Frequencies 115

6.1 Introduction 115

6.2 Simulation of Roughness Profiles 116

6.3 Simulation of Bridges with Rough Surface 117

6.4 Effect of Road Roughness on Vehicle Response 118

6.4.1 Case 1: Vehicle Frequency Less than Any Bridge Frequencies 119

6.4.2 Case 2: Vehicle Frequency Greater than the First Bridge Frequency 119

6.5 Vehicle Responses Induced by Separate Excitational Sources 122

6.6 Closed‐Form Solution of Vehicle Response Considering Road Roughness 122

6.7 Reducing the Impact of Road Roughness by Using Two Connected Vehicles 127

6.8 Numerical Studies 131

6.8.1 Example 1. Two Identical Vehicles Moving over the Bridge of Class A Roughness 131

6.8.2 Example 2. Two Identical Vehicles Moving over the Bridge of Class C Roughness 131

6.8.3 Example 3. Two Vehicles of Identical Frequency but Different Properties 132

6.8.4 Effect of Vehicle Spacing on Identification of Bridge Frequencies 133

6.9 Concluding Remarks 135

7 Filtering Technique for Eliminating the Effect of Road Roughness 137

7.1 Introduction 137

7.2 Numerical Simulations for Vehicle Responses 138

7.3 Filtering Techniques 141

7.3.1 Band‐Pass Filter (BPF)/Band‐Stop Filter (BSF) 141

7.3.2 Singular Spectrum Analysis (SSA) 142

7.3.3 Singular Spectrum Analysis with Band‐Pass Filter (SSA‐BPF) 144

7.4 Case Studies 145

7.4.1 Case 1: Vehicle Frequency Smaller than First Bridge Frequency 145

7.4.2 Case 2: Vehicle Frequency Greater than First Bridge Frequency 148

7.5 Concluding Remarks 151

8 Hand‐Drawn Cart Used to Measure Bridge Frequencies 153

8.1 Introduction 153

8.2 Dynamic Properties of the Hand‐Drawn Test Cart 156

8.3 Basic Dynamic Tests for the Test Cart 157

8.4 Field Tests 162

8.4.1 Effect of Cart Weight 163

8.4.2 Effect of Various Traveling Speeds 165

8.4.3 Various Volumes of Existing Traffic Flows 170

8.5 Concluding Remarks 173

9 Theory for Retrieving Bridge Mode Shapes 175

9.1 Introduction 175

9.2 Hilbert Transformation 176

9.3 Theoretical Formulation 177

9.4 Algorithms and Constraints 181

9.5 Case Studies 185

9.5.1 Test Vehicle Passing through a Bridge with Smooth Road Surface 186

9.5.2 Effect of Vehicle Speed 187

9.5.3 Test Vehicle Traveling along with Random Traffic 190

9.5.4 Effect of Road Surface Roughness 190

9.6 Concluding Remarks 193

10 Contact‐Point Response for Modal Identification of Bridges 195

10.1 Introduction 195

10.2 Theoretical Formulation 197

10.2.1 Dynamic Response of the Vehicle−Bridge Contact Point 198

10.2.2 Dynamic Response of the Moving Vehicle 199

10.2.3 Procedure for Calculating the Contact‐Point Response in a Field Test 201

10.2.4 Relationship Between the Contact‐Point and Vehicle Responses 201

10.3 Finite Element Simulation of VBI Problems 204

10.3.1 Brief on VBI Element 204

10.3.2 Verification of the Theoretical Solution 205

10.4 Retrieval of Bridge Frequencies 206

10.5 Retrieval of Bridge Mode Shapes 208

10.5.1 Effect of Moving Speed 209

10.5.2 Effect of Vehicle Frequency 210

10.6 Effect of Road Roughness 212

10.6.1 Bridge with Rough Surface Free of Existing Traffic 212

10.6.2 Bridge with Rough Surface under Existing Traffic 214

10.7 Concluding Remarks 215

11 Damage Detection of Bridges Using the Contact‐Point Response 217

11.1 Introduction 217

11.2 Dynamic Response of the Vehicle‐Bridge System 219

11.2.1 Contact‐Point Response: Analytical Solution 220

11.2.2 Contact‐Point Response: For Use in Field Test 220

11.3 Algorithm for Damage Detection 221

11.3.1 Hilbert Transformation 221

11.3.2 Strategy for Damage Detection 221

11.4 Finite Element Simulation of the Problem 223

11.4.1 Damage Element for Beams 223

11.4.2 Brief on Vehicle−Bridge Interaction (VBI) Element Used 224

11.5 Detection of Damages on a Beam 225

11.5.1 Detection of Damage Location on the Beam 225

11.5.2 Detection of Damage Severity 226

11.5.3 Detection of Multiple Damages 228

11.6 Parametric Study 228

11.6.1 Effect of Test Vehicle Speed 229

11.6.2 Effect of Measurement Noise 229

11.6.3 Bridge with Rough Surface Free of Random Traffic 230

11.6.4 Bridge with Rough Surface under Random Traffic 232

11.7 Concluding Remarks 234

Appendix: Finite Element Simulation 237

References 247

Author Index 259

Subject Index 265

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