Table of Contents |
1. | Introduction | 1 |
1.1. | Experiencing Dynamics | 1 |
1.2. | Utilize Dynamics | 14 |
1.3. | Dynamics Versus Statics | 19 |
1.4. | Solving Dynamic Problem | 24 |
1.5. | Pioneers of Dynamic Analysis | 29 |
2. | Governing Equation of Motions | 31 |
2.1. | Dynamic Equilibrium | 31 |
2.2. | Principle of Virtual Displacements | 33 |
2.3. | Hamilton's Principle Through Lagrange's Equations | 34 |
2.4. | Momentum Equilibrium | 38 |
2.5. | Validity of Classical Dynamics | 39 |
3. | Free Vibrations for a Single-Degree-of-Freedom (SDOF) System-Translational Oscillations | 41 |
3.1. | Definition of Harmonic Oscillations | 41 |
3.2. | Undamped Free Vibrations of a SDOF System | 42 |
3.3. | Damped Free Vibrations of an SDOF | 47 |
4. | Practical Eigenanalysis and Structural Health Monitoring | 55 |
4.1. | Eigenpairs, Global-, Local- and Rigid-Body Vibrations | 55 |
4.2. | Hand Calculation of Natural Frequency for Systems with Distributed Masses | 58 |
4.2.1. | Classical Method for Exact Solutions | 58 |
4.2.2. | Equivalent System Analysis for Approximate Solutions | 61 |
4.2.3. | Natural Frequency with Distributed Masses: Dunkerley Method for Approximate Solutions | 68 |
4.3. | Using Symmetry and Anti-Symmetry in Eigenanalysis | 72 |
4.4. | Vibration-Based Structural Health Monitoring | 74 |
5. | Solving Eigenproblem for Continuous Systems: Rayleigh Energy Method | 79 |
6. | Vibration and Buckling Under Axial Loading | 87 |
6.1. | Vibration Versus Buckling | 87 |
6.2. | Vibration and Buckling Under Harmonic Axial Loads | 88 |
6.3. | Eigenvalues Under the Influence of Axial Loads | 89 |
7. | Eigenfrequencies of Non-uniform Beams, Shallow-and Deep Foundations | 95 |
7.1. | Non-uniform Beams | 95 |
7.2. | Shallow and Deep Foundations | 97 |
8. | Deterministic and Stochastic Motions | 99 |
8.1. | Category of Motions | 99 |
8.2. | Deterministic Motions | 100 |
8.3. | Random/Stochastic Process | 102 |
9. | Time Domain to Frequency Domain: Spectrum Analysis | 109 |
9.1. | Fourier Spectrum | 109 |
9.2. | Power Spectrum Density | 114 |
10. | Statistics of Motions and Loads | 119 |
10.1. | Narrow- and Wide-Banded Process | 119 |
10.2. | Gaussian Distribution | 121 |
10.3. | Short-Term Distribution for Continuous Random Process: Rayleigh Distribution | 125 |
10.4. | Long-Term Distribution for Continuous Random Process: Weibull distribution | 129 |
10.5. | Number of Occurrence Within a Fixed Time or Space Interval: Poisson Distribution | 132 |
10.6. | Joint Probability Distribution | 134 |
10.7. | Long-Term Prediction | 137 |
10.8. | Environmental Contour Line Method | 138 |
11. | Forced Vibrations | 141 |
11.1. | Forced Vibrations Under Harmonic Excitations | 141 |
11.1.1. | Responses to Harmonic Force | 141 |
11.1.2. | Responses to Harmonic Base Excitations | 152 |
11.2. | Forced Vibrations Under Complex Periodical Excitations | 155 |
11.3. | Forced Vibrations Under Non-periodical Excitations | 156 |
11.3.1. | Transient Responses to Force Excitation with Short Duration | 157 |
11.3.2. | Responses Due to Arbitrary Base Excitations Using Convolution Integral | 161 |
11.3.3. | Responses to Non-Periodical Excitations with Fourier Integral | 162 |
11.4. | Forced Vibrations Under Random Excitations | 164 |
11.4.1. | Method | 164 |
11.4.2. | White Noise Approximation | 169 |
11.5. | Cross-Covariance, Cross-Spectra Density Function and Coherence Function | 170 |
11.5.1. | Cross-Covariance in Time Domain | 170 |
11.5.2. | Cross-Spectra Density in the Frequency Domain | 171 |
11.5.3. | Coherence Function in the Frequency Domain | 171 |
12. | Calculation of Environmental Loading Based on Power Spectra | 173 |
12.1. | Wave Loads | 173 |
12.1.1. | Calculation of Hydrodynamic Wave Loads | 173 |
12.1.2. | Power Spectrum Density for Ocean Wave Kinematics | 175 |
12.2. | Wind Loads | 183 |
12.2.1. | Calculation of Aerodynamic Wind Load | 183 |
12.2.2. | Power Spectrum Density for Wind Velocity Fields | 184 |
12.3. | Ice Loads on Narrow Conical Structures | 196 |
12.4. | Earthquake Ground Motions | 198 |
12.4.1. | Power Spectrum of Seismic Ground Motions | 198 |
12.4.2. | Spatial Variation of Ground Motions by Coherence Function | 200 |
13. | Vibration of Multi-Degrees-of-Freedom Systems | 203 |
13.1. | Equations of Motions | 203 |
13.2. | Free Vibrations of the Two-Degrees-of-Freedom System: Direct/Exact Method | 208 |
13.3. | Forced Vibrations of Two Degrees-of-Freedom Systems: Direct Method | 210 |
13.4. | Forced Vibrations of MDOF: Modal Superposition Method | 211 |
13.5. | Forced Vibrations of MDOF: Direct Time Integration Method | 220 |
13.5.1. | Introduction to the Method | 220 |
13.5.2. | Explicit Integration Method | 224 |
13.5.3. | Implicit Integration Method | 226 |
13.5.4. | Comparison between Modal Superposition and Direct Time Integration Method | 229 |
13.6. | Lumped and Consistent Mass | 230 |
14. | Damping | 233 |
14.1. | Types of Damping and Its Effects | 233 |
14.2. | Damping Modeling | 234 |
14.2.1. | Pure Viscous Damping | 235 |
14.2.2. | Friction/Coulomb Damping | 236 |
14.2.3. | Frequency-Dependent Hysteretic Damping | 238 |
14.2.4. | Frequency-Independent Hysteretic Damping | 240 |
14.2.5. | Fluid (Hydrodynamic or Aerodynamic) Damping | 240 |
14.2.6. | Equivalent Viscous Damping | 241 |
14.2.7. | Equivalent Viscous Damping with Coulomb Damping | 243 |
14.2.8. | Equivalent Viscous Damping with Frequency Dependent Hysteretic Damping | 243 |
14.2.9. | Practical Damping Modeling for Dynamic Analysis | 244 |
14.3. | Measuring Damping | 248 |
14.3.1. | Free Decay Method | 250 |
14.3.2. | Step Response Method | 252 |
14.3.3. | Hysteresis loop method | 253 |
14.3.4. | Amplification-factor Method from Forced Vibrations | 253 |
14.3.5. | Half-power/Bandwidth Method from Forced Vibrations | 254 |
14.4. | Relationship Among Various Expressions of Damping | 255 |
14.5. | Damping for Engineering Structures | 256 |
14.5.1. | Material Damping | 256 |
14.5.2. | Structural/Slip Damping | 257 |
14.5.3. | System Damping | 257 |
14.5.4. | Hydro- and Aerodynamic Damping | 258 |
14.5.5. | Typical Damping Levels | 258 |
14.6. | Comparison of Cyclic Responses Among Structures Made of Elastic, Viscous and Hysteretic (Viscoelastic) Materials | 259 |
15. | Nonlinear Dynamics | 261 |
15.1. | From Linear to Nonlinear | 261 |
15.2. | Sources of Nonlinearities | 263 |
15.2.1. | Material Nonlinearity | 263 |
15.2.2. | Geometrical Nonlinearity | 275 |
15.2.3. | Buckling | 278 |
15.2.4. | Displacement Boundary Nonlinearity | 279 |
15.2.5. | Force Boundary Nonlinearities | 279 |
15.2.6. | Nonlinearities Due to Temperature Effects | 279 |
15.3. | Load Sequence Effects | 280 |
15.4. | Eigenfrequencies Influenced by Nonlinearities | 283 |
15.4.1. | Material Nonlinearity | 283 |
15.4.2. | Geometrical Nonlinearity | 285 |
15.4.3. | P-Delta (P-it) Effects | 288 |
15.5. | Numerical Solutions for Nonlinear Problem | 291 |
15.5.1. | Characteristics of Nonlinear Responses | 291 |
15.5.2. | Load Control (Newton-Type) Methods | 295 |
15.5.3. | Displacement Control Methods | 299 |
15.5.4. | Load-Displacement Control Method-Arc-Length Method (ALM) | 300 |
16. | Structural Responses Due to Seismic Excitations | 303 |
16.1. | Seismic Ground Motions | 303 |
16.1.1. | Transmission of Seismic Wave from Bedrock to Ground | 303 |
16.1.2. | Resonance Period of Soil-Site Period | 304 |
16.1.3. | The Amplitude and Duration of Bedrock Motions | 305 |
16.1.4. | Spatial Variation of Earthquake Ground Motions | 307 |
16.2. | Seismic Response Spectrum | 309 |
16.2.1. | Introduction | 309 |
16.2.2. | Construction of Response Spectrum | 310 |
16.2.3. | Modal Combination Techniques for Response Spectrum Analysis | 312 |
16.3. | Characteristics of Seismic Responses Varying with Frequencies | 314 |
16.4. | Influences from Structures' Orientations and Ice Covering | 316 |
16.5. | Whipping Effects | 317 |
16.6. | Seismic Analysis Methods | 319 |
17. | Fatigue Assessment | 321 |
17.1. | Failure of Structural Components | 321 |
17.2. | Fatigue Damage Assessment | 323 |
17.2.1. | Classification of Fatigue Assessment Approaches | 323 |
17.2.2. | Stress-Based Approach | 324 |
17.2.3. | Strain-Based Approach | 341 |
17.2.4. | Fracture Mechanics Approach | 341 |
17.2.5. | Cumulative Damage | 347 |
17.3. | Dynamic Analysis Methods for Calculating Fatigue Damage | 349 |
17.3.1. | Deterministic Fatigue Analysis Method | 349 |
17.3.2. | Simplified Fatigue Analysis Approach | 351 |
17.3.3. | Stochastic Fatigue Analysis Method with Narrow-Banded Responses | 353 |
17.3.4. | Deterministic vs Stochastic Fatigue Analysis for Structures Subjected to Wave Loads | 360 |
17.3.5. | Fatigue Analysis Methods Accounting for Bandwidth, Multi-modal Frequency and Nonlinearities | 362 |
18. | Human Body Vibrations | 373 |
18.1. | General | 373 |
18.2. | Criteria Related to Human Body Vibrations | 374 |
19. | Vehicle-Structure Interactions | 379 |
19.1. | Introduction to the Topic | 379 |
19.2. | Physical Modeling | 384 |
19.2.1. | General | 384 |
19.2.2. | Vehicle, Lashing and Tire Models | 384 |
19.2.3. | Modeling of Supporting Structures | 391 |
19.2.4. | Interaction Models for Vehicle and Supporting Structures | 393 |
19.3. | Finite Element Simulations | 394 |
19.4. | Analysis of Vehicle Securing | 396 |
| References | 399 |
| Index | 419 |