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 |  موضوع: كتاب Dynamics of Structures - Clough & Penzien السبت 03 أغسطس 2013, 2:02 pm | |
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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 dAlemberts 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 Rayleighs 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 Hamiltons Principle 342
163 Lagranges 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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