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 xvAcknowledgments xixList of Symbols xxiList of Abbreviations xxxi1 Introduction 11.1 Background 11.2 Basic Concept of the VSM for Bridges 31.3 Brief on the Works Conducted by Yang and Coworkers 51.4 Bridge Modal Parameter Identification by Researchers Worldwide 141.5 Bridge Damage Identification by Researchers Worldwide 241.6 Pavement Roughness Identification by Researchers Worldwide 311.7 Vehicle Scanning Method for Railway Tracks and Bridges 321.8 Application of Smartphone-Based IoT System in VSM 371.9 Conclusions and Recommendations for Future Work 39Part I Vehicle Scanning Method for Bridge Frequencies 432 Damped Scanning Vehicle for Bridge Frequencies: Theory and Experiment 452.1 Introduction 452.2 Formulation of the Analytical Theory 472.3 Calculation of Contact Response of the Damped Test Vehicle 512.4 Numerical Formulation of the Problem 542.5 Parametric Study 572.6 Experimental Study 652.7 Concluding Remarks 793 Refined Detection for Bridge Frequencies: Theory and Experiment 813.1 Introduction 813.2 Contact Responses for Two Wheels of Single-Axle Vehicle 843.3 Brief on Test Bridge and Direct Measurement 873.4 Description of Self-Designed Single-Axle Test Vehicle 873.5 Scanning Bridge's Frequencies by Test Vehicle's Rocking Motion 933.6 Concluding Remarks 1004 Single-Axle Two-Mass Scanning Vehicle for Bridge Frequencies: Theory 1034.1 Introduction 1034.2 Analytical Formulation of the Problem 1054.3 Vehicle-Bridge Contact Response of Two-Mass Vehicle Model 1094.4 Numerical Simulation of the Problem 1114.5 Parametric Study 1174.6 Concluding Remarks 1265 Vehicle Scanning Method Enhanced by a Shaker 1275.1 Introduction 1275.2 Theoretical Modeling of the Problem 1295.3 Dynamic Amplification Factor of the Shaker for Vehicle and Contact Responses 1355.4 Numerical Verification 1375.5 Effect of the Shaker on Bridge Frequency Extraction 1415.6 Effects of Pavement Roughness and Environmental Noise 1465.7 Concluding Remarks 1476 Vehicle Scanning Method Enhanced by Amplifiers 1496.1 Introduction 1496.2 Analytical Formulation of the Problem 1526.2.1 Dynamic Responses of the Bridge 1526.3 Effect of Amplifier on the Amplifier-Vehicle-Bridge System 1556.4 Numerical Simulation of the Problem 1596.5 Test Vehicle Set in (or Not in) Resonance 1636.6 Effect of Amplifier on Bridge Frequency Extraction 1656.7 Effect of Pavement Roughness 1686.8 Concluding Remarks 171Part II Vehicle Scanning Method for Bridge Mode Shapes and Damping Ratios 1737 Theory for Scanning Bridge Mode Shapes Using a Two-Axle Vehicle 1757.1 Introduction 1757.2 Closed-Form Solutions for Contact Responses 1777.3 Calculation of Contact Responses for Two-Axle Vehicle 1797.4 Recovery of Bridge Mode Shapes 1817.5 Numerical Verification of Back-Calculated Contact Responses 1847.6 Construction of Bridge Mode Shapes 1887.7 Parametric Study 1907.8 Concluding Remarks 2008 Formula for Determining Damping Ratio Using a Two-Axle Vehicle 2018.1 Introduction 2018.2 Theoretical Formulation of the Problem 2028.3 Determination of Bridge Damping Ratio 2048.4 Numerical Verification 2068.5 Effect of Pavement Roughness 2108.6 Concluding Remarks 2129 Theory for Scanning Bridge Damping Ratios Using a Two-Axle Vehicle by Wavelet Transform 2139.1 Introduction 2139.2 Analytical Formulation of the Problem 2159.3 Calculation of Contact Responses for Two-axle Vehicle Considering Suspension Effect 2189.4 Identification of Bridge Damping Ratio 2219.5 Numerical Verification 2249.6 Scanning Bridge Damping Ratio 2289.7 Parametric Study 2309.8 Concluding Remarks 24310 Normalized Formula for Removing Damping Effect on Mode Shape Recovery 24510.1 Introduction 24510.2 Theoretical Modeling of the Problem 24710.3 Identification of Bridge Mode Shapes with the Effect of Bridge Damping Eliminated 25310.4 Numerical Formulation of the Problem 25510.5 Scanning Bridge Mode Shapes with the Effect of Bridge Damping Eliminated 26010.6 Parametric Study 26110.7 Concluding Remarks 26811 Recursive Formula for Removing Damping Effect on Mode Shape Recovery 26911.1 Introduction 26911.2 Analytical Formulation of the Problem 27111.3 Eliminating the Bridge Damping Effect in Bridge Mode Shape Identification 27511.4 Numerical Verification 27911.5 Parametric Study 28511.6 Concluding Remarks 292Part III Vehicle Scanning Method for Various Types of Bridges 29512 Recovering Frequencies and Mode Shapes of Curved Bridges 29712.1 Introduction 29712.2 Closed-form Solutions for the Horizontal Curved Bridge and Contact Responses 30012.3 Calculation of Contact Responses 30712.4 Mode Shape Construction by the VMD-SWT 30912.5 Numerical Modeling of the Problem 31112.6 Numerical Verification of Mode Shape Construction 31712.7 Parametric Study 31912.8 Concluding Remarks 32313 Recovering Damping Ratios of Curved Bridges 32513.1 Introduction 32513.2 Analytical Solutions for the Damped Horizontal Curved Bridge and Contact Responses 32713.3 Damping Ratio Identification 33613.4 Numerical Modeling of the Problem 33913.5 Damping Ratio Identification for the Curved Bridge by the VMD-SWT 34513.6 Numerical Study 34613.7 Concluding Remarks 35514 Scanning Frequencies and Mode Shapes of Thin-Walled Girders 35714.1 Introduction 35714.2 Theoretical Formulation of the Problem 36014.3 Contact Responses for the Two Wheels of Single-Axle Vehicle 36514.4 Recovery of Bridge's Mode Shapes 36614.5 Numerical Simulation of the Problem 36714.6 Construction of Bridge Mode Shapes 37414.7 Parametric Study 37514.8 Concluding Remarks 38015 Theory for Simultaneously Scanning Modal Properties of Thin-Walled Girders 38115.1 Introduction 38115.2 Theoretical Formulation of the Problem 38315.3 Theoretical Framework for Identification of Bridge Modal Properties 38815.4 Numerical Verification 39515.5 Parametric Study 40215.6 Conclusions 411A L'Hospital's Rule for Deriving Eq. (2.30) 413B VBI Element for Single-DOF Vehicle 415C VBI Element for Two-Axle Vehicle Used in Chapters 7 and 8 419D VBI Element for Two-Axle Vehicle Used in Chapters 9 and 10 421E Straight-Beam Approach for Vibration Analysis of Horizontal Curved Beams 423E.1 Elastic Stiffness and Consistent Mass Matrices of the Straight Beam Element 423E.2 Treatment of Offset between Curved Beam and Straight Beam Element 426E.3 Transformation Matrices 427E.4 Procedure for Calculating Dynamic Responses of Curved Beam 428F VBI Element Used in Chapter 14 429G Coefficients in Eq. (15.7) of Chapter 15 431H VBI Element Used in Chapter 15 433References 435Author Index 457Subject Index 467

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 xvAcknowledgments xixList of Symbols xxiList of Abbreviations xxxi1 Introduction 11.1 Background 11.2 Basic Concept of the VSM for Bridges 31.3 Brief on the Works Conducted by Yang and Coworkers 51.4 Bridge Modal Parameter Identification by Researchers Worldwide 141.5 Bridge Damage Identification by Researchers Worldwide 241.6 Pavement Roughness Identification by Researchers Worldwide 311.7 Vehicle Scanning Method for Railway Tracks and Bridges 321.8 Application of Smartphone-Based IoT System in VSM 371.9 Conclusions and Recommendations for Future Work 39Part I Vehicle Scanning Method for Bridge Frequencies 432 Damped Scanning Vehicle for Bridge Frequencies: Theory and Experiment 452.1 Introduction 452.2 Formulation of the Analytical Theory 472.3 Calculation of Contact Response of the Damped Test Vehicle 512.4 Numerical Formulation of the Problem 542.5 Parametric Study 572.6 Experimental Study 652.7 Concluding Remarks 793 Refined Detection for Bridge Frequencies: Theory and Experiment 813.1 Introduction 813.2 Contact Responses for Two Wheels of Single-Axle Vehicle 843.3 Brief on Test Bridge and Direct Measurement 873.4 Description of Self-Designed Single-Axle Test Vehicle 873.5 Scanning Bridge's Frequencies by Test Vehicle's Rocking Motion 933.6 Concluding Remarks 1004 Single-Axle Two-Mass Scanning Vehicle for Bridge Frequencies: Theory 1034.1 Introduction 1034.2 Analytical Formulation of the Problem 1054.3 Vehicle-Bridge Contact Response of Two-Mass Vehicle Model 1094.4 Numerical Simulation of the Problem 1114.5 Parametric Study 1174.6 Concluding Remarks 1265 Vehicle Scanning Method Enhanced by a Shaker 1275.1 Introduction 1275.2 Theoretical Modeling of the Problem 1295.3 Dynamic Amplification Factor of the Shaker for Vehicle and Contact Responses 1355.4 Numerical Verification 1375.5 Effect of the Shaker on Bridge Frequency Extraction 1415.6 Effects of Pavement Roughness and Environmental Noise 1465.7 Concluding Remarks 1476 Vehicle Scanning Method Enhanced by Amplifiers 1496.1 Introduction 1496.2 Analytical Formulation of the Problem 1526.2.1 Dynamic Responses of the Bridge 1526.3 Effect of Amplifier on the Amplifier-Vehicle-Bridge System 1556.4 Numerical Simulation of the Problem 1596.5 Test Vehicle Set in (or Not in) Resonance 1636.6 Effect of Amplifier on Bridge Frequency Extraction 1656.7 Effect of Pavement Roughness 1686.8 Concluding Remarks 171Part II Vehicle Scanning Method for Bridge Mode Shapes and Damping Ratios 1737 Theory for Scanning Bridge Mode Shapes Using a Two-Axle Vehicle 1757.1 Introduction 1757.2 Closed-Form Solutions for Contact Responses 1777.3 Calculation of Contact Responses for Two-Axle Vehicle 1797.4 Recovery of Bridge Mode Shapes 1817.5 Numerical Verification of Back-Calculated Contact Responses 1847.6 Construction of Bridge Mode Shapes 1887.7 Parametric Study 1907.8 Concluding Remarks 2008 Formula for Determining Damping Ratio Using a Two-Axle Vehicle 2018.1 Introduction 2018.2 Theoretical Formulation of the Problem 2028.3 Determination of Bridge Damping Ratio 2048.4 Numerical Verification 2068.5 Effect of Pavement Roughness 2108.6 Concluding Remarks 2129 Theory for Scanning Bridge Damping Ratios Using a Two-Axle Vehicle by Wavelet Transform 2139.1 Introduction 2139.2 Analytical Formulation of the Problem 2159.3 Calculation of Contact Responses for Two-axle Vehicle Considering Suspension Effect 2189.4 Identification of Bridge Damping Ratio 2219.5 Numerical Verification 2249.6 Scanning Bridge Damping Ratio 2289.7 Parametric Study 2309.8 Concluding Remarks 24310 Normalized Formula for Removing Damping Effect on Mode Shape Recovery 24510.1 Introduction 24510.2 Theoretical Modeling of the Problem 24710.3 Identification of Bridge Mode Shapes with the Effect of Bridge Damping Eliminated 25310.4 Numerical Formulation of the Problem 25510.5 Scanning Bridge Mode Shapes with the Effect of Bridge Damping Eliminated 26010.6 Parametric Study 26110.7 Concluding Remarks 26811 Recursive Formula for Removing Damping Effect on Mode Shape Recovery 26911.1 Introduction 26911.2 Analytical Formulation of the Problem 27111.3 Eliminating the Bridge Damping Effect in Bridge Mode Shape Identification 27511.4 Numerical Verification 27911.5 Parametric Study 28511.6 Concluding Remarks 292Part III Vehicle Scanning Method for Various Types of Bridges 29512 Recovering Frequencies and Mode Shapes of Curved Bridges 29712.1 Introduction 29712.2 Closed-form Solutions for the Horizontal Curved Bridge and Contact Responses 30012.3 Calculation of Contact Responses 30712.4 Mode Shape Construction by the VMD-SWT 30912.5 Numerical Modeling of the Problem 31112.6 Numerical Verification of Mode Shape Construction 31712.7 Parametric Study 31912.8 Concluding Remarks 32313 Recovering Damping Ratios of Curved Bridges 32513.1 Introduction 32513.2 Analytical Solutions for the Damped Horizontal Curved Bridge and Contact Responses 32713.3 Damping Ratio Identification 33613.4 Numerical Modeling of the Problem 33913.5 Damping Ratio Identification for the Curved Bridge by the VMD-SWT 34513.6 Numerical Study 34613.7 Concluding Remarks 35514 Scanning Frequencies and Mode Shapes of Thin-Walled Girders 35714.1 Introduction 35714.2 Theoretical Formulation of the Problem 36014.3 Contact Responses for the Two Wheels of Single-Axle Vehicle 36514.4 Recovery of Bridge's Mode Shapes 36614.5 Numerical Simulation of the Problem 36714.6 Construction of Bridge Mode Shapes 37414.7 Parametric Study 37514.8 Concluding Remarks 38015 Theory for Simultaneously Scanning Modal Properties of Thin-Walled Girders 38115.1 Introduction 38115.2 Theoretical Formulation of the Problem 38315.3 Theoretical Framework for Identification of Bridge Modal Properties 38815.4 Numerical Verification 39515.5 Parametric Study 40215.6 Conclusions 411A L'Hospital's Rule for Deriving Eq. (2.30) 413B VBI Element for Single-DOF Vehicle 415C VBI Element for Two-Axle Vehicle Used in Chapters 7 and 8 419D VBI Element for Two-Axle Vehicle Used in Chapters 9 and 10 421E Straight-Beam Approach for Vibration Analysis of Horizontal Curved Beams 423E.1 Elastic Stiffness and Consistent Mass Matrices of the Straight Beam Element 423E.2 Treatment of Offset between Curved Beam and Straight Beam Element 426E.3 Transformation Matrices 427E.4 Procedure for Calculating Dynamic Responses of Curved Beam 428F VBI Element Used in Chapter 14 429G Coefficients in Eq. (15.7) of Chapter 15 431H VBI Element Used in Chapter 15 433References 435Author Index 457Subject Index 467