Vehicle-Bridge Interaction Dynamics

Transcription

1 Vehicle-Bridge Interaction Dynamics With Applications to High-Speed Railways Y. B. Yang National Taiwan University, Taiwan J. D. Yau Tamkang University, Taiwan Y. S. Wu Sinotech Engineering Consultants, Ltd., Taiwan World Scientific NEW JERSEY LONDON SINGAPORE BEIJING' SHANGHAI HONGKONG TAIPEI CHENNAI

2 Contents Preface Acknowledgments List of Symbols xv xxi xxiii 1. Introduction Major Considerations Vehicle Models Bridge Models Railway Bridges and Vehicles Methods of Solution Impact Factor and Speed Parameter Concluding Remarks 22 Part I Moving Load Problems Impact Response of Simply-Supported Beams Introduction Simple Beam Subjected to a Single Moving Load Impact Factor for Midpoint Displacement Impact Factor for Midpoint Bending Moment Impact Factor for End Shear Force Simple Beam Subjected to a Series of Moving Loads 45

3 vi Vehicle-Bridge Interaction Dynamics Modeling of Wheel Loads of a Train Method of Solution Phenomenon of Resonance Phenomenon of Cancellation Optimal Design Criteria Illustrative Examples Comparison with Finite Element Solutions Effects of Moving Masses and Damping Effect of Span to Car Length Ratio Concluding Remarks Impact Response of Railway Bridges with Elastic Bearings Introduction Equation of Motion Fundamental Frequency of the Beam Dynamic Response Analysis Phenomena of Resonance and Cancellation Effect of Structural Damping Envelope Formula for Resonance Response Impact Factor and Envelope Impact Formulas Numerical Examples Phenomenon of Resonance Effect of Structural Damping Envelope Impact Formula Concluding Remarks Mechanism of Resonance and Cancellation for Elastically-Supported Beams Introduction Formulation of the Theory Assumed Modal Shape of Vibration Single Moving Load A Series of Moving Loads Conditions of Resonance and Cancellation Mechanism of Resonance and Cancellation 112

4 Contents vii 4.5 Field Measurement of Vibration of Railway Bridges Concluding Remarks Curved Beams Subjected to Vertical and Horizontal Moving Loads Introduction Governing Differential Equations Curved Beam Subjected to a Single Moving Load Vertical Moving Load Horizontal Moving Load Unified Expressions for Vertical and Radial Vibrations Solutions for Multi Moving Loads Conditions of Resonance and Cancellation Numerical Examples Comparison of Analytic with Finite Element Solutions Phenomenon of Cancellation Under Single or Multi Moving Masses Phenomenon of Resonance Under Multi Moving Masses IS Plot Impact Effect Caused by Moving Loads Concluding Remarks 152 Part II Interaction Dynamics Problems Vehicle Bridge Interaction Element Based on Dynamic Condensation Introduction Equations of Motion for the Vehicle and Bridge Element Equations in Incremental Form Equivalent Stiffness Equation for Vehicles Vehicle-Bridge Interaction Element 165

5 viii Vehicle-Bridge Interaction Dynamics 6.6 Incremental Dynamic Analysis with Iterations Equivalent Stiffness Equations for VBI System Procedure of Iterations Numerical Verification Simple Beam Subjected to Moving Sprung Mass Simple Beam Subjected to Moving Train Free-Fixed Beam with Various Models for Moving Vehicles Parametric Studies Models for Bridge, Train and Rail Irregularities Moving Load versus Sprung Mass Model Effect of Rail Irregularities Effect of Ballast Stiffness Effect of Vehicle Suspension Stiffness Effect of Vehicle Suspension Damping Concluding Remarks Vehicle-Bridge Interaction Element Considering Pitching Effect Introduction Equations of Motion for the Vehicle and Bridge Rigid Vehicle-Bridge Interaction Element Equations of Motion for the VBI System Numerical Studies Simple Beam Traveled by a Two-Axle System Simple Beam Traveled by a Train Consisting of Five Identical Cars Riding Comfort in the Presence of Track Irregularities 223

6 Contents ix Effect of Elasticity of the Suspension System Effect of Damping of the Suspension System Effect of Track Irregularity Concluding Remarks 229 Modeling of Vehicle Bridge Interactions by the Concept of Contact Forces Introduction Vehicle Equations and Contact Forces Solution of Contact Forces from Vehicle Equations VBI Element Considering Vertical Contact Forces Only VBI Element Considering General Contact Forces System Equations and Structural Damping Procedure of Time-History Analysis for VBI Systems Numerical Examples and Verification Cantilever Beam Subjected to a Moving Load Cantilever Beam Subjected to a Moving Mass Simple Beam Subjected to a Moving Sprung Mass Simple Beam Subjected to a Moving Rigid Bar Supported by Spring-Dashpot Units Bridge Subjected to a Vehicle in Deceleration Bridges Subjected to a Train Consisting of 10 Identical Cars Concluding Remarks 268

7 x Vehicle-Bridge Interaction Dynamics 9. Vehicle-Rails-Bridge Interaction Two-Dimensional Modeling Introduction Train and Bridge Models and Minimal Bridge Segment Vehicle's Equations of Motion and Contact Forces Rails and Bridge Element Equations Central Finite Rail (CFR) Element and Bridge Element Left Semi-Infinite Rail (LSR) Element Right Semi-Infinite Rail (RSR) Element VRI Element Considering Vertical Contact Forces Only VRI Element Considering General Contact Forces System Equations and Structural Damping Shift of Bridge Segment and Renumbering of Nodal Degrees of Freedom Verification of Proposed Procedure Numerical Studies Steady-State Responses of the Train, Rails and Bridge Impact Response of Rails and Bridge Under Various Train Speeds Response of Train to Track Irregularity and Riding Comfort of Train Effect of the Track System Concluding Remarks Vehicle-Rails-Bridge Interaction Three-Dimensional Modeling Introduction Three-Dimensional Models for Train, Track and Bridge 313

8 Contents xi 10.3 Vehicle Equations and Contact Forces Equations for the Rail and Bridge Elements Central Finite Rail (CFR) Element for Track A Central Finite Rail (CFR) Element for Track B The Bridge Element Left Semi-Infinite Rail (LSR) Element for Track A Right Semi-Infinite Rail (RSR) Element for Track A Left Semi-Infinite Rail (LSR) Element for Track B Right Semi-Infinite Rail (RSR) Element for Track B VRI Element Considering Vertical and Lateral Contact Forces VRI Element Considering General Contact Forces System Equations and Structural Damping Simulation of Track Irregularities Verification of the Proposed Theory and Procedure Dynamic Characteristics of Train-Rails-Bridge Systems Properties of the Railway Vehicles and Bridge Natural Frequencies of the Railway Vehicles and Bridge Dynamic Interactions Between the Train and Bridge Train-Rails-Bridge Interaction Considering Track Irregularities Dynamic Effects Induced by Trains at Different Speeds Response Induced by Two Trains in Crossing

9 xii Vehicle-Bridge Interaction Dynamics Criteria for Derailment and Safety Assessment of Trains Concluding Remarks Stability of Trains Moving over Bridges Shaken by Earthquakes Introduction Analysis Model for Train-Rails-Bridge System Railway-Bridge System with Ground Motions Central Finite Rail (CFR) Element for Track A Central Finite Rail (CFR) Element for Track B Bridge Element Left Semi-Infinite Rail (LSR) Element for Tracks A and B Right Semi-Infinite Rail (RSR) Element for Tracks A and B Method of Analysis Description of Input Earthquake Records Train Resting on Railway Bridge under Earthquake Responses of Bridge and Train Car Contact Forces between Wheels and Rails Maximum YQ Ratio for Wheelsets in Earthquake Stability of an Idle Train under Earthquakes of Various Intensities Trains Moving over Railway Bridges under Earthquakes Responses of Bridge and Train Car Maximum YQ Ratio for Moving Trains in Earthquake Stability Assessment of Moving Trains in Earthquake Concluding Remarks 470

10 Contents xiii Appendix A Derivation of Response Function P\ in Eq. (2.55) 473 Appendix B Newmark's (3 Method 477 Appendix C Appendix D Appendix E Appendix F Appendix G Appendix H Appendix I Appendix J Vertical Frequency of Vibration of Curved Beam 481 Horizontal Frequency of Vibration of Curved Beam 483 Derivation of Residual Vibration for Curved Beam in Eq. (5.53) 485 Beam Element and Structural Damping Matrix 489 F.I Equation of Motion for Beam Element F.2 Structural Damping Matrix 493 Partitioned Matrices and Vector for Vehicle, Eq. (9.4) 497 Related Matrices and Vectors for CFR Element 501 Related Matrices and Vectors for 3D Vehicle Model 503 Mass and Stiffness Matrices for Rail and Bridge Elements 507 J.I Mass and Stiffness Matrices of the CFR Element for Both Tracks 507 J.2 Mass and Stiffness Matrices of the Bridge Element 508

11 xiv Vehicle-Bridge Interaction Dynamics J.3 Mass and Stiffness Matrices for the LSR Element 509 J.4 Mass and Stiffness Matrices of the RSR Element 510 J.5 Related Matrices and Vectors for the Rail Elements 510 References 513 Subject Index 527