كتاب Dynamics of Structures - Clough & Penzien
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 كتاب Dynamics of Structures - Clough & Penzien

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عدد المساهمات : 14261
التقييم : 22948
تاريخ التسجيل : 01/07/2009
العمر : 28
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
الجامعة : المنوفية

مُساهمةموضوع: كتاب Dynamics of Structures - Clough & Penzien   السبت 03 أغسطس 2013, 2:02 pm

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أحضرت لكم كتاب
Dynamics of Structures - Clough & Penzien
RayW. Clough
Professor of Civil Engineering
University of California, Berkeley
Joseph Penzien
International Civil Engineering
Consultants, Inc.
THIRD EDITION


ويتناول الموضوعات الأتية :

1 Overview of Structural Dynamics 1
1­1 Fundamental Objective of Structural Dynamics Analysis 1
1­2 Types of Prescribed Loadings 2
1­3 Essential Characteristics of a Dynamic Problem 3
1­4 Methods of Discretization 4
Lumped­Mass Procedure 4
Generalized Displacements 5
The Finite­Element Concept 7
1­5 Formulation of the Equations of Motion 9
Direct Equilibration using dŠAlembertŠs Principle 9
Principle of Virtual Displacements 10
Variational Approach 10
1­6 Organization of the Text 11
PART I SINGLE­DEGREE­OF­FREEDOM SYSTEMS
2 Analysis of Free Vibrations 15
2­1 Components of the Basic Dynamic System 15
2­2 Equation of Motion of the Basic Dynamic System 16
2­3 Inuence of Gravitational Forces 17
2­4 Inuence of Support Excitation 18
2­5 Analysis of Undamped Free Vibrations 20
2­6 Damped Free Vibrations 25
Critically­Damped Systems 26
Undercritically­Damped Systems 27
Overcritically­Damped Systems 32
Problems 32
3­1 Undamped System 33
Complementary Solution 33
Particular Solution 33
General Solution 34
3­2 System with Viscous Damping 36
3­3 Resonant Response 42
3­4 Accelerometers and Displacement Meters 45
3­5 Vibration Isolation 46
3­6 Evaluation of Viscous­Damping Ratio 52
Free­Vibration Decay Method 52
Resonant Amplication Method 53
Half­Power (Band­Width) Method 54
Resonance Energy Loss Per Cycle Method 56
3­7 Complex­Stiffness Damping 58
Problems 61
4 Response to Periodic Loading 65
4­1 Fourier Series Expressions of Periodic Loading 65
Trigonometric Form 65
Exponential Form 66
4­2 Response to the Fourier Series Loading 67
4­3 Preview of Frequency­Domain Analysis 69
Problems 71
5 Response to Impulsive Loading 73
5­1 General Nature of Impulsive Loading 73
5­2 Sine­Wave Impulse 74
5­3 Rectangular Impulse 77
5­4 Triangular Impulse 78
5­5 Shock or Response Spectra 79
5­6 Approximate Analysis of Impulsive­Load Response 82
Problems 84
6 Response to General Dynamic Loading: Superposition Methods 87
6­1 Analysis Through the Time Domain 87
Formulation of Response Integral 87
Numerical Evaluation of Response Integral 89
6­2 Analysis Through the Frequency Domain 97
Fourier Response Integral 98
Discrete Fourier Transforms (DVF) 100
CONTENTS vii
Fast Fourier Transforms (FFT) 102
Evaluation of Dynamic Response 106
6­3 Relationship between the Time­ and Frequency­Domain
Transfer Functions 109
Problems 109
7 Response to General Dynamic Loading: Step­by­Step Methods 111
7­1 General Concepts 111
7­2 Piecewise Exact Method 112
7­3 Numerical Approximation Procedures General Comments 116
7­4 Second Central Difference Formulation 117
7­5 Integration Methods 120
Euler­Gauss Procedure 120
Newmark Beta Methods 121
Conversion to Explicit Formulation 123
7­6 Incremental Formulation for Nonlinear Analysis 124
7­7 Summary of the Linear Acceleration Procedure 127
Problems 132
8 Generalized Single­Degree­of­Freedom Systems 133
8­1 General Comments on SDOF Systems 133
8­2 Generalized Properties: Assemblages of Rigid Bodies 134
8­3 Generalized Properties: Distributed Flexibility 140
8­4 Expressions for Generalized System Properties 145
8­5 Vibration Analysis by RayleighŠs Method 149
8­6 Selection of the Rayleigh Vibration Shape 152
8­7 Improved Rayleigh Method 156
Problems 160
PART II MULTI­DEGREE­OF­FREEDOM SYSTEMS
9 Formulation of the MDOF Equations of Motion 169
9­1 Selection of the Degrees of Freedom 169
9­2 Dynamic­Equilibrium Condition 171
9­3 Axial­Force Effects 173
10 Evaluation of Structural­Property Matrices 175
10­1 Elastic Properties 175
Flexibility 175
Stiffness 176
Basic Structural Concepts 177
Finite­Element Stiffness 179
viii CONTENTS
10­2 Mass Properties 184
Lumped­Mass Matrix 184
Consistent­Mass Matrix 185
10­3 Damping Properties 189
10­4 External Loading 189
Static Resultants 190
Consistent Nodal Loads 190
10­5 Geometric Stiffness 191
Linear Approximation 191
Consistent Geometric Stiffness 194
10­6 Choice of Property Formulation 196
Problems 198
11 Undamped Free Vibrations 201
11­1 Analysis of Vibration Frequencies 201
11­2 Analysis of Vibration Mode Shapes 204
11­3 Flexibility Formulation of Vibration Analysis 208
11­4 Inuence of Axial Forces 208
Free Vibrations 208
Buckling Load 209
Buckling with Harmonic Excitation 210
11­5 Orthogonality Conditions 211
Basic Conditions 211
Additional Relationships 212
Normalizing 214
Problems 215
12 Analysis of Dynamic Response Using Superposition 219
12­1 Normal Coordinates 219
12­2 Uncoupled Equations of Motion: Undamped 221
12­3 Uncoupled Equations of Motion: Viscous Damping 222
12­4 Response Analysis by Mode Displacement Superposition 223
Viscous Damping 223
Complex­Stiffness Damping 230
12­5 Construction of Proportional Viscous Damping Matrices 234
Rayleigh Damping 234
Extended Rayleigh Damping 237
Alternative Formulation 240
Construction of Nonproportional Damping Matrices 242
12­6 Response Analysis using Coupled Equations of Motion 245
Time Domain 245
CONTENTS ix
Frequency Domain 246
12­7 Relationship between Time­ and Frequency­ Domain
Transfer Functions 247
12­8 Practical Procedure for solving Coupled Equations of Motion 251
12­9 Interpolation Procedure for Generation of Transfer Functions 254
Problems 256
13 Vibration Analysis by Matrix Iteration 259
13­1 Preliminary Comments 259
13­2 Fundamental Mode Analysis 260
13­3 Proof of Convergence 265
13­4 Analysis of Higher Modes 267
Second­Mode Analysis 267
Analysis of Third and Higher Modes 271
Analysis of Highest Mode 272
13­5 Buckling Analysis by Matrix Iteration 275
13­6 Inverse Iteration the Preferred Procedure 279
13­7 Inverse Iteration with Shifts 281
13­8 Special Eigenproblem Topics 285
Eigenproperty Expansion 286
Symmetric Form of Dynamic Matrix 288
Analysis of Unconstrained Structures 290
Problems 291
14 Selection of Dynamic Degrees of Freedom 293
14­1 Finite­Element Degrees of Freedom 293
One­Dimensional Elements 294
Two­ and Three­Dimensional Elements 294
14­2 Kinematic Constraints 295
14­3 Static Condensation 296
14­4 Rayleigh Method in Discrete Coordinates 298
14­5 Rayleigh­Ritz Method 299
14­6 Subspace Iteration 304
14­7 Reduction of Modal Truncation Errors 306
General Comments on Coordinate Reduction 306
Modal Contributions 307
Static Correction Procedure 311
Mode Acceleration Method 313
14­8 Derived Ritz Vectors 314
Preliminary Comments 314
Derivation Details 316
x CONTENTS
Tridiagonal Equations of Motion 319
Loss of Orthogonality 322
Required Number of Vectors 323
Problems 323
15 Analysis of MDOF Dynamic Response: Step­by­Step Methods 325
15­1 Preliminary Comments 325
15­2 Incremental Equations of Motion 327
15­3 Step­by­Step Integration: Constant Average Acceleration Method 328
15­4 Step­by­Step Integration: Linear Acceleration Method 330
15­5 Strategies for Analysis of Coupled MDOF Systems 332
Localized Nonlinearity 332
Coupled Effects Treated as Pseudo­Forces 336
16 Variational Formulation of the Equations of Motion 341
16­1 Generalized Coordinates 341
16­2 HamiltonŠs Principle 342
16­3 LagrangeŠs Equations of Motion 344
16­4 Derivation of the General Equations of Motion for Linear Systems 351
16­5 Constraints and Lagrange Multipliers 356
Problems 359
PART III DISTRIBUTED­PARAMETER SYSTEMS
17 Partial Differential Equations of Motion 365
17­1 Introduction 365
17­2 Beam Flexure: Elementary Case 366
17­3 Beam Flexure: Including Axial­Force Effects 368
17­4 Beam Flexure: Including Viscous Damping 369
17­5 Beam Flexure: Generalized Support Excitations 370
17­6 Axial Deformations: Undamped 373
Problems 375
18 Analysis of Undamped Free Vibrations 377
18­1 Beam Flexure: Elementary Case 377
18­2 Beam Flexure: Including Axial­Force Effects 386
18­3 Beam Flexure: With Distributed Elastic Support 388
18­4 Beam Flexure: Orthogonality of Vibration Mode Shapes 389
18­5 Free Vibrations in Axial Deformation 391
18­6 Orthogonality of Axial Vibration Modes 392
Problems 394
CONTENTS xi
19 Analysis of Dynamic Response 397
19­1 Normal Coordinates 397
19­2 Uncoupled Flexural Equations of Motion: Undamped Case 400
19­3 Uncoupled Flexural Equations of Motion: Damped Case 403
19­4 Uncoupled Axial Equations of Motion: Undamped Case 407
19­5 Wave­Propagation Analysis 411
Basic Axial­Wave­Propagation Equation 411
Consideration of Boundary Conditions 415
Discontinuity in Bar Properties 418
Problems 423
PART IV RANDOM VIBRATIONS
20 Probability Theory 427
20­1 Single Random Variable 427
20­2 Important Averages of a Single Random Variable 432
20­3 One­Dimensional Random Walk 434
20­4 Two Random Variables 442
20­5 Important Averages of Two Random Variables 451
20­6 Scatter Diagram and Correlation of Two Random Variables 455
20­7 Principal Axes of Joint Probability Density Function 458
20­8 Rayleigh Probability Density Function 461
20­9 m Random Variables 463
20­10 Linear Transformations of Normally Distributed Random Variables 465
Problems 466
21 Random Processes 471
21­1 Denition 471
21­2 Stationary and Ergodic Processes 473
21­3 Autocorrelation Function for Stationary Processes 478
21­4 Power Spectral Density Function for Stationary Processes 484
21­5 Relationship Between Power Spectral Density and Autocorrelation
Functions 485
21­6 Power Spectral Density and Autocorrelation Functions for Derivatives
of Processes 488
21­7 Superposition of Stationary Processes 490
21­8 Stationary Gaussian Processes: One Independent Variable 492
21­9 Stationary White Noise 498
21­10 Probability Distribution for Maxima 501
21­11 Probability Distribution for Extreme Values 506
21­12 Nonstationary Gaussian Processes 510
21­13 Stationary Gaussian Process: Two or More Independent Variables 511
xii CONTENTS
Problems 512
22 Stochastic Response of Linear SDOF Systems 517
22­1 Transfer Functions 517
22­2 Relationship between Input and Output Autocorrelation Functions 518
22­3 Relationship between Input and Output Power Spectral
Density Functions 522
22­4 Response Characteristics for Narrowband Systems 524
22­5 Nonstationary Mean Square Response Resulting from Zero Initial
Conditions 528
22­6 Fatigue Predictions for Narrowband Systems 532
Problems 535
23 Stochastic Response of Linear MDOF Systems 539
23­1 Time­Domain Response for Linear Systems using Normal Modes 539
23­2 Frequency­Domain Response for Linear Systems using Normal Modes 541
23­3 Normal Mode Forcing Function due to Discrete Loadings 543
23­4 Normal Mode Forcing Function due to Distributed Loadings 547
23­5 Frequency­Domain Response for Linear Systems having Frequency­
Dependent Parameters and/or Coupled Normal Modes 548
Problems 550
PART V EARTHQUAKE ENGINEERING
24 Seismological Background 555
24­1 Introductory Note 555
24­2 Seismicity 556
24­3 Earthquake Faults and Waves 558
24­4 Structure of the Earth 559
24­5 Plate Tectonics 563
24­6 Elastic­Rebound Theory of Earthquakes 567
24­7 Measures of Earthquake Size 571
25 Free­Field Surface Ground Motions 575
25­1 Fourier and Response Spectra 575
25­2 Factors inuencing Response Spectra 581
25­3 Design Response Spectra 586
Dual Strategy of Seismic Design 586
Peak Ground Accelerations 587
Response Spectrum Shapes 590
Uniform­Hazard Site­Specic Response Spectra 595
Two Horizontal Components of Motion 597
CONTENTS xiii
25­4 Design Accelerograms 597
Response Spectrum Compatible Accelerograms 598
Principal Axes of Motion 603
Spatially Correlated Motions 607
26 Deterministic Earthquake Response: Systems on Rigid Foundations613
26­1 Types of Earthquake Excitation 613
26­2 Response to Rigid­Soil Excitations 615
Lumped SDOF Elastic Systems, Translational Excitation 615
Generalized­Coordinate SDOF Elastic Systems, Translational
Excitation 617
Lumped MDOF Elastic Systems, Translational Excitation 623
Comparison with ATC­3 Recommended Code Provisions 638
Distributed­Parameter Elastic Systems, Translational Excitation 640
Lumped MDOF Elastic Systems, Rotational Excitation 642
Lumped MDOF Elastic Systems, Multiple Excitation 644
Lumped SDOF Elastic­Plastic Systems, Translational Excitation 647
26­3 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 Two­Component­Excitation Responses 657
Problems 662
27 Deterministic Earthquake Response: Including Soil­Structure
Interaction 669
27­1 Soil­Structure Interaction by Direct Analysis 669
Kinematic Interaction for Translational Excitation; the Tau Effect 670
Direct Inclusion of a Bounded Soil Layer 673
27­2 Substructure Analysis of SSI Response 674
Lumped SDOF Systems on Rigid Mat Foundation 674
General MDOF System with Multiple Support Excitation 679
Generation of Boundary Impedances 689
27­3 Response of Underground Structures 704
Free­Field Ground Motions due to Propagating Plane Waves 704
Racking Deformations of Cross Sections 705
Overall Axial and Flexural Deformations 706
Inuence of Transverse Joints on Axial Deformations 709
28 Stochastic Structural Response 711
28­1 Modeling of Strong Ground Motions 711
xiv CONTENTS
28­2 Stochastic Response of Linear Systems 711
SDOF Systems 711
MDOF Systems 712
28­3 Extreme­Value Response of Nonlinear Systems 713
SDOF Systems 713
MDOF Systems 723
28­4 Design Considerations 726
28­5 Allowable Ductility Demand Versus Ductility Capacity 729
Index 731


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