TY - BOOK AU - Clough,Ray W. AU - Penzien,Joseph TI - Dynamics of structures / SN - 0070113947 PY - 1993/// CY - New York PB - McGraw-Hill KW - STRUCTURAL DYNAMICS KW - FREE VIBRATIONS KW - HARMONIC LOADING KW - PERIODIC LOADING KW - IMPULSIVE LOADING KW - SUPERPOSITION METHODS KW - STEP-BY STEP-METHOD KW - CARGA DINAMICA KW - DINAMICA-ESTRUCTURAS KW - DINAMICA ESTRUCTURAL N1 - CONTENIDO Preface xv List of Symbols xvii 1. Overview of Structural Dynamics 1 Fundamental Objective of Structural Dynamics Analysis 1 Types of Prescribed Loadings 2 Essential Characteristics of a Dynamic Problem 3 Methods of Discretization 4 Lumped-Mass Procedure 4 Generalized Displacements 5 The Finite-Element Concept 7 Formulation of the Equations of Motion 9 Direct Equilibration using d´Alembert´s Principle 9 Principle of Virtual Displacements 10 Variation al Approach 10 PART I. SINGLE-DEGREE-OF-FREEDOM SYSTEMS 2 2. Analysis of Free Vibrations 15 Components of the Basic Dynamic System 15 Equation of Motion of the Basic Dynamic System 16 Influence of Gravitational Forces 17 Influence of Support Excitation 18 Analysis of Undraped Free Vibrations 20 Damped Free Vibrations 25 Critically-Damped Systems 26 Under critically-Damped Systems 27 Over critically-Damped Systems 32 3. Response to Harmonic Loading 33 Undraped System 33 Complementary Solution 33 Particular Solution 33 General Solution 34 System with Viscous Damping 36 Resonant Response 42 Accelerometers and Displacement Meters 45 Vibration Isolation 46 Evaluation of Viscous-Damping Ratio 52 Free-Vibration Decay Method 52 Resonant Amplification Method 53 Half-Power (Band-Width) Method 54 Resonance Energy Loss per Cycle Method 56 Complex-Stiffness Damping 58 4. Response to Periodic Loading 65 Fourier series Expressions of Periodic Loading 65 Trigonometric Form 65 Exponential Form 66 Response to the Fourier series Loading 67 Preview of Frequency-Domain Analysis 69 5. Response to Impulsive Loading 73 General Nature of Impulsive Loading 73 Sine-Wave Impulse 74 Rectangular Impulse 77 Triangular Impulse 78 Shock or Response Spectra 79 Approximate Analysis of Impulsive-Load Response 82 6. Response to General Dynamic Loading: Superposition Methods 87 Analysis through the Time Domain 87 Formulation of Response Integral 87 Numerical Evaluation of Response Integral 89 Analysis through the Frequency Domain 97 Fourier Response Integral 98 Discrete Fourier Transforms (DVF) 100 Fast Fourier Transforms (FFT) 102 Evaluation of Dynamic Response 106 Relationship between the Time- and Frequency-Domain Transfer Functions 109 7. Response to General Dynamic Loading: Step-by-Step Methods 111 General Concepts 111 Piecewise Exact Method 112 Numerical Approximation Procedures General Comments 116 Second Central Difference Formulation 117 Integration Methods 120 Euler-Gauss Procedure 120 New mark Beta Methods 121 Conversion to Explicit Formulation 123 Incremental Formulation for Nonlinear Analysis 124 Summary of the Linear Acceleration Procedure 127 8. Generalized Single-Degree-of-Freedom Systems 133 General Comments on SDOF Systems 133 Generalized Properties: Assemblages of Rigid Bodies 134 Generalized Properties: Distributed Flexibility 140 Expressions for Generalized System Properties 145 Vibration Analysis by Rayleigh's Method 149 Selection of the Rayleigh Vibration Shape 152 Improved Rayleigh Method 156 PART II. MULTI-DEGREE-OF-FREEDOM SYSTEMS 159 9. Formulation of the MDOF Equations of Motion 169 Selection of the Degrees of Freedom 169 Dynamic-Equilibrium Condition 171 Axial-Force Effects 173 10. Evaluation of Structural-Property Matrices 175 Elastic Properties 175 Flexibility 175 Stiffness 176 Basic Structural Concepts 177 Finite-Element Stiffness 179 Mass Properties 184 Lumped-Mass Matrix 184 Consistent-Mass Matrix 185 Damping Properties 189 External Loading 189 Static Resultants 190 Consistent Nodal Loads 190 Geometric Stiffness 191 Linear Approximation 191 Consistent Geometric Stiffness 194 Choice of Property Formulation 196 Undamped Free Vibrations 201 Analysis of Vibration Frequencies 201 Analysis of Vibration Mode Shapes 204 Flexibility Formulation of Vibration Analysis 208 Influence of Axial Forces 208 Free Vibrations 208 Buckling Load 209 Buckling with Harmonic Excitation 210 Orthogonality Conditions 211 Basic Conditions 211 Additional Relationships 212 Normalizing 214 12. Analysis of Dynamic Response Using Superposition 219 Normal Coordinates 219 Uncoupled Equations of Motion: Undamped 221 Uncoupled Equations of Motion: Viscous Damping 222 Response Analysis by Mode Displacement Superposition 223 Viscous Damping 223 Complex-Stiffness Damping 230 Construction of Proportional Viscous Damping Matrices 234 Rayleigh Damping 234 Extended Rayleigh Damping 237 Alternative Formulation 240 Construction of Nonproportional Damping Matrices 242 Response Analysis using Coupled Equations of Motion 245 Time Domain 245 Frequency Domain 246 Relationship between Time- and Frequency- Domain Transfer Functions 247 Practical Procedure for solving Coupled Equations of Motion 251 Interpolation Procedure for Generation of Transfer Functions 254 13. Vibration Analysis by Matrix Iteration 259 Preliminary Comments 259 Fundamental Mode Analysis 260 Proof of Convergence 265 Analysis of Higher Modes 267 Second-Mode Analysis 267 Analysis of Third and Higher Modes 271 Analysis of Highest Mode 272 Buckling Analysis by Matrix Iteration 275 Inverse Iteration the Preferred Procedure 279 Inverse Iteration with Shifts 281 Special Eigenproblem Topics 285 Eigenproperty Expansion 286 Symmetric Form of Dynamic Matrix 288 Analysis of Unconstrained Structures 290 14. Selection of Dynamic Degrees of Freedom 293 Finite-Element Degrees of Freedom 293 One-Dimensional Elements 294 Two- and Three-Dimensional Elements 294 Kinematic Constraints 295 Static Condensation 296 Rayleigh Method in Discrete Coordinates 298 Rayleigh-Ritz Method 299 Subspace Iteration 304 Reduction of Modal Truncation Errors 306 General Comments on Coordinate Reduction 306 Modal Contributions 307 Static Correction Procedure 311 Mode Acceleration Method 313 Derived Ritz Vectors 314 Preliminary Comments 314 Derivation Details 316 Tridiagonal Equations of Motion 319 Loss of Orthogonality 322 Required Number of Vectors 323 15. Analysis of MDOF Dynamic Response: Step-by-Step Methods 325 Preliminary Comments 325 Incremental Equations of Motion 327 Step-by-Step Integration: Constant Average Acceleration Method 328 Step-by-Step Integration: Linear Acceleration Method 330 Strategies for Analysis of Coupled MDOF Systems 332 Localized Nonlinearity 332 Coupled Effects Treated as Pseudo-Forces 336 16. Variational Formulation of the Equations of Motion 341 Generalized Coordinates 341 Hamilton's Principle 342 Lagrange's Equations of Motion 344 Derivation of the General Equations of Motion for Linear Systems 351 Constraints and Lagrange Multipliers 356 PART III. DISTRIBUTED-PARAMETER SYSTEMS 17. Partial Differential Equations of Motion 365 Beam Flexure: Elementary Case 366 Beam Flexure: Including Axial-Force Effects 368 Beam Flexure: Including Viscous Damping 369 Beam Flexure: Generalized Support Excitations 370 Axial Deformations: Undamped 373 18. Analysis of Undamped Free Vibrations 377 Beam Flexure: Elementary Case 377 Beam Flexure: Including Axial-Force Effects 386 Beam Flexure: With Distributed Elastic Support 388 Beam Flexure: Orthogonality of Vibration Mode Shapes 389 Free Vibrations in Axial Deformation 391 Orthogonality of Axial Vibration Modes 392 19. Analysis of Dynamic Response 397 Normal Coordinates 397 Uncoupled Flexural Equations of Motion: Undamped Case 400 Uncoupled Flexural Equations of Motion: Damped Case 403 Uncoupled Axial Equations of Motion: Undamped Case 407 Wave-Propagation Analysis 411 Basic Axial-Wave-Propagation Equation 411 Consideration of Boundary Conditions 415 Discontinuity in Bar Properties 418 PART IV. RANDOM VIBRATIONS 20. Probability Theory 427 Single Random Variable 427 Important Averages of a Single Random Variable 432 One-Dimensional Random Walk 434 Two Random Variables 442 Important Averages of Two Random Variables 451 Scatter Diagram and Correlation of Two Random Variables 455 Principal Axes of Joint Probability Density Function 458 Rayleigh Probability Density Function 461 Random Variables 463 Linear Transformations of Normally Distributed Random Variables 465 21. Random Processes 471 Definition 471 Stationary and Ergodic Processes 473 Autocorrelation Function for Stationary Processes 478 Power Spectral Density Function for Stationary Processes 484 Relationship Between Power Spectral Density and Autocorrelation Functions 485 Power Spectral Density and Autocorrelation Functions for Derivatives of Processes 488 Superposition of Stationary Processes 490 Stationary Gaussian Processes: One Independent Variable 492 Stationary White Noise 498 Probability Distribution for Maxima 501 Probability Distribution for Extreme Values 506 Nonstationary Gaussian Processes 510 Stationary Gaussian Process: Two or More Independent Variables 511 22. Stochastic Response of Linear SDOF Systems 517 Transfer Functions 517 Relationship between Input and Output Autocorrelation Functions 518 Relationship between Input and Output Power Spectral Density Functions 522 Response Characteristics for Narrowband Systems 524 Nonstationary Mean Square Response Resulting from Zero Initial Conditions 528 Fatigue Predictions for Narrowband Systems 532 23. Stochastic Response of Linear MDOF Systems 539 Time-Domain Response for Linear Systems using Normal Modes 539 Frequency-Domain Response for Linear Systems using Normal Modes 541 Normal Mode Forcing Function due to Discrete Loadings 543 Normal Mode Forcing Function due to Distributed Loadings 547 Frequency-Domain Response for Linear Systems having Frequency-Dependent Parameters and/or Coupled Normal Modes 548 PART V. EARTHQUAKE ENGINEERING 24. Seismological Background 555 Introductory Note 555 Seismicity 556 Earthquake Faults and Waves 558 Structure of the Earth 559 Plate Tectonics 563 Elastic-Rebound Theory of Earthquakes 567 Measures of Earthquake Size 571 25. Free-Field Surface Ground Motions 575 Fourier and Response Spectra 575 Factors influencing Response Spectra 581 Design Response Spectra 586 Dual Strategy of Seismic Design 586 Peak Ground Accelerations 587 Response Spectrum Shapes 590 Uniform-Hazard Site-Specific Response Spectra 595 Two Horizontal Components of Motion 597 Design Accelerograms 597 Response Spectrum Compatible Accelerograms 598 Principal Axes of Motion 603 Spatially Correlated Motions 607 26. Deterministic Earthquake Response: Systems on Rigid Foundations 613 Types of Earthquake Excitation 613 Response to Rigid-Soil Excitations 615 Lumped SDOF Elastic Systems, Translational Excitation 615 Generalized-Coordinate SDOF Elastic Systems, Translational Excitation 617 Lumped MDOF Elastic Systems, Translational Excitation 623 Comparison with ATC-3 Recommended Code Provisions 638 Distributed-Parameter Elastic Systems, Translational Excitation 640 Lumped MDOF Elastic Systems, Rotational Excitation 642 Lumped MDOF Elastic Systems, Multiple Excitations 644 Lumped SDOF Elastic-Plastic Systems, Translational Excitation 647 Combining Maximum Modal Responses 650 Mean Square Response of a Single Mode 650 Covariance of Response Produced by Two Modes 652 SRSS and CQC Combination of Modal Responses 653 Combining Two-Component-Excitation Responses 657 27. Deterministic Earthquake Response: Including Soil-Structure 660 Soil-Structure Interaction by Direct Analysis 669 Kinematic Interaction for Translational Excitation; the Tau Effect 670 Direct Inclusion of a Bounded Soil Layer 673 Substructure Analysis of SSI Response 674 Lumped SDOF Systems on Rigid Mat Foundation 674 General MDOF System with Multiple Support Excitations 679 Generation of Boundary Impedances 689 Response of Underground Structures 704 Free-Field Ground Motions due to Propagating Plane Waves 704 Racking Deformations of Cross Sections 705 Overall Axial and Flexural Deformations 706 Influence of Transverse Joints on Axial Deformations 709 28. Stochastic Structural Response 711 Modeling of Strong Ground Motions 711 Stochastic Response of Linear Systems 711 SDOF Systems 711 MDOF Systems 712 Extreme-Value Response of Nonlinear Systems 713 SDOF Systems 713 MDOF Systems 723 Design Considerations 726 Allowable Ductility Demand versus Ductility Capacity 729 Index 731 ER -