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Framework for scanning modal parameters of bridges from vehicle responses utilizing the Vehicle Scanning Method (VSM)
Advanced Vehicle Scanning Method: Bridge Modal Parameter Identification delivers a complete theoretical framework for scanning of the modal parameters (frequencies, damping ratios, and mode shapes) of bridges from vehicle responses. This book provides comprehensive coverage of the application of the Vehicle Scanning Method (VSM) for different types of bridges, which has the advantage of mobility, economy, and efficiency over the conventional, direct method.
Most of the materials presented in each chapter have been published as technical papers in high-ranking international journals, which were subjected to critical reviews. The contents of the book have been arranged such that they are reflective of the progressive advancement of the VSM technique.
Edited by a highly qualified team of authors including one of the original developers of the VSM technique, Advanced Vehicle Scanning Method includes information on:
Advanced Vehicle Scanning Method is an essential reference on the subject for researchers working on bridge dynamics, graduate students in programs of study related to vehicle-bridge interaction, and practicing bridge engineers.
Dr. Hao Xu is an Associate Professor at the School of Civil Engineering, Chongqing University, China. In 2023, he was awarded the Young Elite Scientists Sponsorship Program by the China Association for Science and Technology (CAST).
Dr. Der-Shen Yang is an Associate Professor at the College of Civil Engineering, Tongji University, China. In 2024, he was awarded the Excellent Young Scientists Fund Program (Overseas) by the National Natural Science Foundation of China.
Dr. Yeong-Bin Yang is Honorary Dean of the School of Civil Engineering, Chongqing University, China. He is a member of the Chinese Academy of Engineering and the European Academy of Sciences and Arts, and a foreign member of the Austrian Academy of Sciences.
Preface xv
Acknowledgments xix
List of Symbols xxi
List of Abbreviations xxxi
1 Introduction 1
1.1 Background 1
1.2 Basic Concept of the VSM for Bridges 3
1.3 Brief on the Works Conducted by Yang and Coworkers 5
1.4 Bridge Modal Parameter Identification by Researchers Worldwide 14
1.5 Bridge Damage Identification by Researchers Worldwide 24
1.6 Pavement Roughness Identification by Researchers Worldwide 31
1.7 Vehicle Scanning Method for Railway Tracks and Bridges 32
1.8 Application of Smartphone-Based IoT System in VSM 37
1.9 Conclusions and Recommendations for Future Work 39
Part I Vehicle Scanning Method for Bridge Frequencies 43
2 Damped Scanning Vehicle for Bridge Frequencies: Theory and Experiment 45
2.1 Introduction 45
2.2 Formulation of the Analytical Theory 47
2.3 Calculation of Contact Response of the Damped Test Vehicle 51
2.4 Numerical Formulation of the Problem 54
2.5 Parametric Study 57
2.6 Experimental Study 65
2.7 Concluding Remarks 79
3 Refined Detection for Bridge Frequencies: Theory and Experiment 81
3.1 Introduction 81
3.2 Contact Responses for Two Wheels of Single-Axle Vehicle 84
3.3 Brief on Test Bridge and Direct Measurement 87
3.4 Description of Self-Designed Single-Axle Test Vehicle 87
3.5 Scanning Bridge's Frequencies by Test Vehicle's Rocking Motion 93
3.6 Concluding Remarks 100
4 Single-Axle Two-Mass Scanning Vehicle for Bridge Frequencies: Theory 103
4.1 Introduction 103
4.2 Analytical Formulation of the Problem 105
4.3 Vehicle-Bridge Contact Response of Two-Mass Vehicle Model 109
4.4 Numerical Simulation of the Problem 111
4.5 Parametric Study 117
4.6 Concluding Remarks 126
5 Vehicle Scanning Method Enhanced by a Shaker 127
5.1 Introduction 127
5.2 Theoretical Modeling of the Problem 129
5.3 Dynamic Amplification Factor of the Shaker for Vehicle and Contact Responses 135
5.4 Numerical Verification 137
5.5 Effect of the Shaker on Bridge Frequency Extraction 141
5.6 Effects of Pavement Roughness and Environmental Noise 146
5.7 Concluding Remarks 147
6 Vehicle Scanning Method Enhanced by Amplifiers 149
6.1 Introduction 149
6.2 Analytical Formulation of the Problem 152
6.2.1 Dynamic Responses of the Bridge 152
6.3 Effect of Amplifier on the Amplifier-Vehicle-Bridge System 155
6.4 Numerical Simulation of the Problem 159
6.5 Test Vehicle Set in (or Not in) Resonance 163
6.6 Effect of Amplifier on Bridge Frequency Extraction 165
6.7 Effect of Pavement Roughness 168
6.8 Concluding Remarks 171
Part II Vehicle Scanning Method for Bridge Mode Shapes and Damping Ratios 173
7 Theory for Scanning Bridge Mode Shapes Using a Two-Axle Vehicle 175
7.1 Introduction 175
7.2 Closed-Form Solutions for Contact Responses 177
7.3 Calculation of Contact Responses for Two-Axle Vehicle 179
7.4 Recovery of Bridge Mode Shapes 181
7.5 Numerical Verification of Back-Calculated Contact Responses 184
7.6 Construction of Bridge Mode Shapes 188
7.7 Parametric Study 190
7.8 Concluding Remarks 200
8 Formula for Determining Damping Ratio Using a Two-Axle Vehicle 201
8.1 Introduction 201
8.2 Theoretical Formulation of the Problem 202
8.3 Determination of Bridge Damping Ratio 204
8.4 Numerical Verification 206
8.5 Effect of Pavement Roughness 210
8.6 Concluding Remarks 212
9 Theory for Scanning Bridge Damping Ratios Using a Two-Axle Vehicle by Wavelet Transform 213
9.1 Introduction 213
9.2 Analytical Formulation of the Problem 215
9.3 Calculation of Contact Responses for Two-axle Vehicle Considering Suspension Effect 218
9.4 Identification of Bridge Damping Ratio 221
9.5 Numerical Verification 224
9.6 Scanning Bridge Damping Ratio 228
9.7 Parametric Study 230
9.8 Concluding Remarks 243
10 Normalized Formula for Removing Damping Effect on Mode Shape Recovery 245
10.1 Introduction 245
10.2 Theoretical Modeling of the Problem 247
10.3 Identification of Bridge Mode Shapes with the Effect of Bridge Damping Eliminated 253
10.4 Numerical Formulation of the Problem 255
10.5 Scanning Bridge Mode Shapes with the Effect of Bridge Damping Eliminated 260
10.6 Parametric Study 261
10.7 Concluding Remarks 268
11 Recursive Formula for Removing Damping Effect on Mode Shape Recovery 269
11.1 Introduction 269
11.2 Analytical Formulation of the Problem 271
11.3 Eliminating the Bridge Damping Effect in Bridge Mode Shape Identification 275
11.4 Numerical Verification 279
11.5 Parametric Study 285
11.6 Concluding Remarks 292
Part III Vehicle Scanning Method for Various Types of Bridges 295
12 Recovering Frequencies and Mode Shapes of Curved Bridges 297
12.1 Introduction 297
12.2 Closed-form Solutions for the Horizontal Curved Bridge and Contact Responses 300
12.3 Calculation of Contact Responses 307
12.4 Mode Shape Construction by the VMD-SWT 309
12.5 Numerical Modeling of the Problem 311
12.6 Numerical Verification of Mode Shape Construction 317
12.7 Parametric Study 319
12.8 Concluding Remarks 323
13 Recovering Damping Ratios of Curved Bridges 325
13.1 Introduction 325
13.2 Analytical Solutions for the Damped Horizontal Curved Bridge and Contact Responses 327
13.3 Damping Ratio Identification 336
13.4 Numerical Modeling of the Problem 339
13.5 Damping Ratio Identification for the Curved Bridge by the VMD-SWT 345
13.6 Numerical Study 346
13.7 Concluding Remarks 355
14 Scanning Frequencies and Mode Shapes of Thin-Walled Girders 357
14.1 Introduction 357
14.2 Theoretical Formulation of the Problem 360
14.3 Contact Responses for the Two Wheels of Single-Axle Vehicle 365
14.4 Recovery of Bridge's Mode Shapes 366
14.5 Numerical Simulation of the Problem 367
14.6 Construction of Bridge Mode Shapes 374
14.7 Parametric Study 375
14.8 Concluding Remarks 380
15 Theory for Simultaneously Scanning Modal Properties of Thin-Walled Girders 381
15.1 Introduction 381
15.2 Theoretical Formulation of the Problem 383
15.3 Theoretical Framework for Identification of Bridge Modal Properties 388
15.4 Numerical Verification 395
15.5 Parametric Study 402
15.6 Conclusions 411
A L'Hospital's Rule for Deriving Eq. (2.30) 413
B VBI Element for Single-DOF Vehicle 415
C VBI Element for Two-Axle Vehicle Used in Chapters 7 and 8 419
D VBI Element for Two-Axle Vehicle Used in Chapters 9 and 10 421
E Straight-Beam Approach for Vibration Analysis of Horizontal Curved Beams 423
E.1 Elastic Stiffness and Consistent Mass Matrices of the Straight Beam Element 423
E.2 Treatment of Offset between Curved Beam and Straight Beam Element 426
E.3 Transformation Matrices 427
E.4 Procedure for Calculating Dynamic Responses of Curved Beam 428
F VBI Element Used in Chapter 14 429
G Coefficients in Eq. (15.7) of Chapter 15 431
H VBI Element Used in Chapter 15 433
References 435
Author Index 457
Subject Index 467
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