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Advanced Structural Dynamics [Kõva köide]

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Eduardo Kausel (Massachusetts Institute of Technology)

Formaat: Hardback, 744 pages, kõrgus x laius x paksus: 262x183x40 mm, kaal: 1740 g
Ilmumisaeg: 07-Aug-2017
Kirjastus: Cambridge University Press
ISBN-10: 1107171512
ISBN-13: 9781107171510

Teised raamatud teemal:

Structural engineering

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Formaat: Hardback, 744 pages, kõrgus x laius x paksus: 262x183x40 mm, kaal: 1740 g
Ilmumisaeg: 07-Aug-2017
Kirjastus: Cambridge University Press
ISBN-10: 1107171512
ISBN-13: 9781107171510

Teised raamatud teemal:

Structural engineering

Püsilink: https://www.kriso.ee/db/9781107171510.html

Märksõnad:

Developed from three decades' worth of lecture notes which the author used to teach at the Massachusetts Institute of Technology, this unique textbook presents a comprehensive treatment of structural dynamics and mechanical vibration. The chapters in this book are self-contained so that instructors can choose to be selective about which topics they teach. Written with an application-based focus, the text covers topics such as earthquake engineering, soil dynamics, and relevant numerical methods techniques that use MATLAB. Advanced topics such as the Hilbert transform, gyroscope forces, and spatially periodic structures are also treated extensively. Concise enough for an introductory course yet rigorous enough for an advanced or graduate-level course, this textbook is also a useful reference manual - even after the final exam - for professional and practicing engineers.

Developed from three decades' worth of lecture notes from Massachusetts Institute of Technology lectures, this concise textbook presents an exhaustive treatment of structural dynamics and mechanical vibration. Appropriate for introductory courses yet rigorous enough for advanced courses, this book is for graduate students, doctoral candidates, practicing professionals, and instructors.

Muu info

Based on the author's lectures at the Massachusetts Institute of Technology, this concise textbook presents an exhaustive treatment of structural dynamics and mechanical vibration.

Preface

xxi

Notation and Symbols

xxv

Unit Conversions

xxix

1 Fundamental Principles

(54)

1.1 Classification of Problems in Structural Dynamics

(1)

1.2 Stress-Strain Relationships

(1)

1.2.1 Three-Dimensional State of Stress-Strain

(1)

1.2.2 Plane Strain

(1)

1.2.3 Plane Stress

(1)

1.2.4 Plane Stress versus Plane Strain: Equivalent Poisson's Ratio

(1)

1.3 Stiffnesses of Some Typical Linear Systems

(8)

1.4 Rigid Body Condition of Stiffness Matrix

(1)

1.5 Mass Properties of Rigid, Homogeneous Bodies

(5)

1.6 Estimation of Miscellaneous Masses

(3)

1.6.1 Estimating the Weight (or Mass) of a Building

(1)

1.6.2 Added Mass of Fluid for Fully Submerged Tubular Sections

(2)

1.6.3 Added Fluid Mass and Damping for Bodies Floating in Deep Water

(1)

1.7 Degrees of Freedom

(2)

1.7.1 Static Degrees of Freedom

(1)

1.7.2 Dynamic Degrees of Freedom

(1)

1.8 Modeling Structural Systems

(9)

1.8.1 Levels of Abstraction

(3)

1.8.2 Transforming Continuous Systems into Discrete Ones

(1)

Heuristic Method

(1)

1.8.3 Direct Superposition Method

(1)

1.8.4 Direct Stiffness Approach

(1)

1.8.5 Flexibility Approach

(2)

1.8.6 Viscous Damping Matrix

(2)

1.9 Fundamental Dynamic Principles for a Rigid Body

(8)

1.9.1 Inertial Reference Frames

(1)

1.9.2 Kinematics of Motion

(3)

Cardanian Rotation

(1)

Eulerian Rotation

(1)

1.9.3 Rotational Inertia Forces

(1)

1.9.4 Newton's Laws

(1)

a Rectilinear Motion

(1)

b Rotational Motion

(1)

1.9.5 Kinetic Energy

(1)

1.9.6 Conservation of Linear and Angular Momentum

(1)

a Rectilinear Motion

(1)

b Rotational Motion

(1)

1.9.7 D'Alembert's Principle

(1)

1.9.8 Extension of Principles to System of Particles and Deformable Bodies

(1)

1.9.9 Conservation of Momentum versus Conservation of Energy

(1)

1.9.10 Instability of Rigid Body Spinning Freely in Space

(1)

1.10 Elements of Analytical Mechanics

(16)

1.10.1 Generalized Coordinates and Its Derivatives

(2)

1.10.2 Lagrange's Equations

(13)

a Elastic Forces

(1)

b Damping Forces

(1)

c External Loads

(1)

d Inertia Forces

(1)

e Combined Virtual Work

(10)

2 Single Degree of Freedom Systems

(76)

2.1 The Damped SDOF Oscillator

(12)

2.1.1 Free Vibration: Homogeneous Solution

(3)

Underdamped Case (xi < 1)

(1)

Critically Damped Case (xi = 1)

(1)

Overdamped Case (xi > 1)

(1)

2.1.2 Response Parameters

(1)

2.1.3 Homogeneous Solution via Complex Frequencies: System Poles

(1)

2.1.4 Free Vibration of an SDOF System with Time-Varying Mass

(2)

2.1.5 Free Vibration of SDOF System with Frictional Damping

(4)

a System Subjected to Initial Displacement

(1)

b Arbitrary Initial Conditions

(2)

2.2 Phase Portrait: Another Way to View Systems

(6)

2.2.1 Preliminaries

(2)

2.2.2 Fundamental Properties of Phase Lines

(2)

Trajectory Arrows

(1)

Intersection of Phase Lines with Horizontal Axis

(1)

Asymptotic Behavior at Singular Points and Separatrix

(1)

Period of Oscillation

(1)

2.2.3 Examples of Application

(2)

Phase Lines of a Linear SDOF System

(1)

Ball Rolling on a Smooth Slope

(2)

2.3 Measures of Damping

(3)

2.3.1 Logarithmic Decrement

(1)

2.3.2 Number of Cycles to 50% Amplitude

(1)

2.3.3 Other Forms of Damping

(1)

2.4 Forced Vibrations

(9)

2.4.1 Forced Vibrations: Particular Solution

(3)

a Heuristic Method

(1)

b Variation of Parameters Method

(1)

2.4.2 Forced Vibrations: General Solution

(1)

2.4.3 Step Load of Infinite Duration

(1)

2.4.4 Step Load of Finite Duration (Rectangular Load, or Box Load)

(1)

2.4.5 Impulse Response Function

(2)

2.4.6 Arbitrary Forcing Function: Convolution

(2)

Convolution Integral

(1)

Time Derivatives of the Convolution Integral

(1)

Convolution as a Particular Solution

(1)

2.5 Support Motion in SDOF Systems

(7)

2.5.1 General Considerations

(3)

2.5.2 Response Spectrum

(1)

Tripartite Spectrum

(1)

2.5.3 Ship on Rough Seas, or Car on Bumpy Road

(3)

2.6 Harmonic Excitation: Steady-State Response

(14)

2.6.1 Transfer Function Due to Harmonic Force

(4)

2.6.2 Transfer Function Due to Harmonic Support Motion

(4)

2.6.3 Eccentric Mass Vibrator

100

(2)

Experimental Observation

101

(1)

2.6.4 Response to Suddenly Applied Sinusoidal Load

102

(1)

2.6.5 Half-Power Bandwidth Method

103

(3)

Application of Half-Power Bandwidth Method

105

(1)

2.7 Response to Periodic Loading

106

(9)

2.7.1 Periodic Load Cast in Terms of Fourier Series

106

(1)

2.7.2 Nonperiodic Load as Limit of Load with Infinite Period

107

(2)

2.7.3 System Subjected to Periodic Loading: Solution in the Time Domain

109

(2)

2.7.4 Transfer Function versus Impulse Response Function

111

(1)

2.7.5 Fourier Inversion of Transfer Function by Contour Integration

111

(3)

Location of Poles, Fourier Transforms, and Causality

113

(1)

2.7.6 Response Computation in the Frequency Domain

114

(1)

1 Trailing Zeros

115

(1)

2 Exponential Window Method: The Preferred Strategy

115

(1)

2.8 Dynamic Stiffness or Impedance

115

(3)

2.8.1 Connection of Impedances in Series and/or Parallel

117

(1)

Standard Solid

118

(1)

2.9 Energy Dissipation through Damping

118

(13)

2.9.1 Viscous Damping

119

(4)

Instantaneous Power and Power Dissipation

119

(1)

Human Power

120

(1)

Average Power Dissipated in Harmonic Support Motion

120

(1)

Ratio of Energy Dissipated to Energy Stored

121

(1)

Hysteresis Loop for Spring-Dashpot System

122

(1)

2.9.2 Hysteretic Damping

123

(1)

Ratio of Energy Dissipated to Energy Stored

123

(1)

Instantaneous Power and Power Dissipation via the Hilbert Transform

124

(1)

2.9.3 Power Dissipation during Broadband Base Excitation

124

(1)

2.9.4 Comparing the Transfer Functions for Viscous and Hysteretic Damping

125

(2)

Best Match between Viscous and Hysteretic Oscillator

126

(1)

2.9.5 Locus of Viscous and Hysteretic Transfer Function

127

(4)

3 Multiple Degree of Freedom Systems

131

(120)

3.1 Multidegree of Freedom Systems

131

(10)

3.1.1 Free Vibration Modes of Undamped MDOF Systems Orthogonality Conditions

132

(2)

Normalized Eigenvectors

134

(1)

3.1.2 Expansion Theorem

134

(3)

3.1.3 Free Vibration of Undamped System Subjected to Initial Conditions

137

(1)

3.1.4 Modal Partition of Energy in an Undamped MDOF System

137

(1)

3.1.5 What If the Stiffness and Mass Matrices Are Not Symmetric?

138

(1)

3.1.6 Physically Homogeneous Variables and Dimensionless Coordinates

139

(2)

3.2 Effect of Static Loads on Structural Frequencies: H-is Effects

141

(5)

3.2.1 Effective Lateral Stiffness

141

(3)

3.2.2 Vibration of Cantilever Column under Gravity Loads

144

(1)

3.2.3 Buckling of Column with Rotations Prevented

145

(1)

3.2.4 Vibration of Cantilever Shear Beam

146

(1)

3.3 Estimation of Frequencies

146

(16)

3.3.1 Rayleigh Quotient

147

(2)

Rayleigh-Schwarz Quotients

149

(1)

3.3.2 Dunkerley-Mikhlin Method

149

(8)

Dunkerley's Method for Systems with Rigid-Body Modes

154

(3)

3.3.3 Effect on Frequencies of a Perturbation in the Structural Properties

157

(5)

Perturbation of Mass Matrix

158

(1)

Perturbation of Stiffness Matrix

159

(1)

Qualitative Implications of Perturbation Formulas

160

(2)

3.4 Spacing Properties of Natural Frequencies

162

(14)

3.4.1 The Minimax Property of Rayleigh's Quotient

162

(3)

3.4.2 Interlacing of Eigenvalues for Systems with Single External Constraint

165

(2)

Single Elastic External Support

166

(1)

3.4.3 Interlacing of Eigenvalues for Systems with Single Internal Constraint

167

(1)

Single Elastic Internal Constraint

167

(1)

3.4.4 Number of Eigenvalues in Some Frequency Interval

167

(9)

Sturm Sequence Property

167

(1)

The Sign Count of the Shifted Stiffness Matrix

168

(2)

Root Count for Dynamically Condensed Systems

170

(3)

Generalization to Continuous Systems

173

(3)

3.5 Vibrations of Damped MDOF Systems

176

(20)

3.5.1 Vibrations of Proportionally Damped MDOF Systems

176

(5)

3.5.2 Proportional versus Nonproportional Damping Matrices

181

(1)

3.5.3 Conditions under Which a Damping Matrix Is Proportional

181

(2)

3.5.4 Bounds to Coupling Terms in Modal Transformation

183

(1)

3.5.5 Rayleigh Damping

184

(1)

3.5.6 Caughey Damping

185

(4)

3.5.7 Damping Matrix Satisfying Prescribed Modal Damping Ratios

189

(2)

3.5.8 Construction of Nonproportional Damping Matrices

191

(3)

3.5.9 Weighted Modal Damping: The Biggs-Roesset Equation

194

(2)

3.6 Support Motions in MDOF Systems

196

(13)

3.6.1 Structure with Single Translational DOF at Each Mass Point

197

(3)

Solution by Modal Superposition (Proportional Damping)

198

(2)

3.6.2 MDOF System Subjected to Multicomponent Support Motion

200

(3)

3.6.3 Number of Modes in Modal Summation

203

(2)

3.6.4 Static Correction

205

(2)

3.6.5 Structures Subjected to Spatially Varying Support Motion

207

(2)

3.7 Nonclassical, Complex Modes

209

(14)

3.7.1 Quadratic Eigenvalue Problem

210

(1)

3.7.2 Poles or Complex Frequencies

210

(3)

3.7.3 Doubled-Up Form of Differential Equation

213

(2)

3.7.4 Orthogonality Conditions

215

(1)

3.7.5 Modal Superposition with Complex Modes

216

(5)

3.7.6 Computation of Complex Modes

221

(2)

3.8 Frequency Domain Analysis of MDOF Systems

223

(15)

3.8.1 Steady-State Response of MDOF Systems to Structural Loads

223

(1)

3.8.2 Steady-State Response of MDOF System Due to Support Motion

224

(7)

3.8.3 In-Phase, Antiphase, and Opposite-Phase Motions

231

(2)

3.8.4 Zeros of Transfer Functions at Point of Application of Load

233

(1)

3.8.5 Steady-State Response of Structures with Hysteretic Damping

234

(1)

3.8.6 Transient Response of MDOF Systems via Fourier Synthesis

235

(1)

3.8.7 Decibel Scale

236

(1)

3.8.8 Reciprocity Principle

236

(2)

3.9 Harmonic Vibrations Due to Vortex Shedding

238

(1)

3.10 Vibration Absorbers

239

(12)

3.10.1 Tuned Mass Damper

239

(4)

3.10.2 Lanchester Mass Damper

243

(1)

3.10.3 Examples of Application of Vibration Absorbers

244

(5)

3.10.4 Torsional Vibration Absorber

249

(2)

4 Continuous Systems

251

(82)

4.1 Mathematical Characteristics of Continuous Systems

251

(9)

4.1.1 Taut String

251

(1)

4.1.2 Rods and Bars

252

(1)

4.1.3 Bending Beam, Rotational Inertia Neglected

252

(2)

4.1.4 Bending Beam, Rotational Inertia Included

254

(1)

4.1.5 Timoshenko Beam

254

(2)

4.1.6 Plate Bending

256

(1)

4.1.7 Vibrations in Solids

257

(1)

4.1.8 General Mathematical Form of Continuous Systems

258

(1)

4.1.9 Orthogonality of Modes in Continuous Systems

259

(1)

4.2 Exact Solutions for Simple Continuous Systems

260

(45)

4.2.1 Homogeneous Rod

260

(7)

Normal Modes of a Finite Rod

262

(1)

Fixed-Fixed Rod

262

(1)

Free-Free Rod

263

(1)

Fixed-Free Rod

264

(1)

Normal Modes of a Rod without Solving a Differential Equation

264

(1)

Orthogonality of Rod Modes

265

(2)

4.2.2 Euler-Bernoulli Beam (Bending Beam)

267

(7)

Normal Modes of a Finite-Length Euler-Bernoulli Beam

268

(1)

Simply Supported Beam

269

(1)

Other Boundary Conditions

269

(1)

Normal Modes of a Free-Free Beam

270

(3)

Normal Modes of a Cantilever Beam

273

(1)

Orthogonality Conditions of a Bending Beam

274

(1)

Strain and Kinetic Energies of a Beam

274

(1)

4.2.3 Bending Beam Subjected to Moving Harmonic Load

274

(3)

Homogeneous Solution

275

(1)

Particular Solution

275

(2)

4.2.4 Nonuniform Bending Beam

277

(2)

4.2.5 Nonclassical Modes of Uniform Shear Beam

279

(8)

Dynamic Equations of Shear Beam

280

(1)

Modes of Rotationally Unrestrained Shear Beam

281

(6)

Concluding Observations

287

(1)

4.2.6 Inhomogeneous Shear Beam

287

(5)

Solution for Shear Modulus Growing Unboundedly with Depth

288

(1)

Finite Layer of Inhomogeneous Soil

289

(1)

Special Case: Shear Modulus Zero at Free Surface

290

(1)

Special Case: Linearly Increasing Shear Wave Velocity

291

(1)

4.2.7 Rectangular Prism Subjected to SH Waves

292

(3)

Normal Modes

292

(1)

Forced Vibration

293

(2)

4.2.8 Cones, Frustums, and Horns

295

(7)

a Exponential Horn

296

(3)

b Frustum Growing as a Power of the Axial Distance

299

(2)

c Cones of Infinite Depth with Bounded Growth of Cross Section

301

(1)

4.2.9 Simply Supported, Homogeneous, Rectangular Plate

302

(3)

Orthogonality Conditions of General Plate

302

(1)

Simply Supported, Homogeneous Rectangular Plate

303

(2)

4.3 Continuous, Wave-Based Elements (Spectral Elements)

305

(28)

4.3.1 Impedance of a Finite Rod

306

(5)

4.3.2 Impedance of a Semi-infinite Rod

311

(1)

4.3.3 Viscoelastic Rod on a Viscous Foundation (Damped Rod)

311

(7)

Stress and Velocity

313

(1)

Power Flow

314

(4)

4.3.4 Impedance of a Euler Beam

318

(4)

4.3.5 Impedance of a Semi-infinite Beam

322

(1)

4.3.6 Infinite Euler Beam with Springs at Regular Intervals

323

(5)

Cutoff Frequencies

326

(1)

Static Roots

327

(1)

4.3.7 Semi-infinite Euler Beam Subjected to Bending Combined with Tension

328

(5)

Power Transmission

331

(1)

Power Transmission after Evanescent Wave Has Decayed

331

(2)

5 Wave Propagation

333

(38)

5.1 Fundamentals of Wave Propagation

333

(15)

5.1.1 Waves in Elastic Bodies

333

(1)

5.1.2 Normal Modes and Dispersive Properties of Simple Systems

334

(8)

An Infinite Rod

334

(2)

Gravity Waves in a Deep Ocean

336

(1)

An Infinite Bending Beam

337

(1)

A Bending Beam on an Elastic Foundation

338

(2)

A Bending Beam on an Elastic Half-Space

340

(1)

Elastic Thick Plate (Mindlin Plate)

341

(1)

5.1.3 Standing Waves, Wave Groups, Group Velocity, and Wave Dispersion

342

(3)

Standing Waves

342

(1)

Groups and Group Velocity

343

(1)

Wave Groups and the Beating Phenomenon

344

(1)

Summary of Concepts

344

(1)

5.1.4 Impedance of an Infinite Rod

345

(3)

5.2 Waves in Layered Media via Spectral Elements

348

(23)

5.2.1 SH Waves and Generalized Love Waves

349

(9)

A Normal Modes

353

(2)

B Source Problem

355

(1)

C Wave Amplification Problem

355

(3)

5.2.2 SV-P Waves and Generalized Rayleigh Waves

358

(4)

Normal Modes

362

(1)

5.2.3 Stiffness Matrix Method in Cylindrical Coordinates

362

(3)

5.2.4 Accurate Integration of Wavenumber Integrals

365

(6)

Maximum Wavenumber for Truncation and Layer Coupling Static Asymptotic Behavior: Tail of Integrals

367

(2)

Wavenumber Step

369

(2)

6 Numerical Methods

371

(110)

6.1 Normal Modes by Inverse Iteration

371

(7)

6.1.1 Fundamental Mode

371

(3)

6.1.2 Higher Modes: Gram-Schmidt Sweeping Technique

374

(1)

6.1.3 Inverse Iteration with Shift by Rayleigh Quotient

374

(2)

6.1.4 Improving Eigenvectors after Inverse Iteration

376

(1)

6.1.5 Inverse Iteration for Continuous Systems

377

(1)

6.2 Method of Weighted Residuals

378

(6)

6.2.1 Point Collocation

381

(1)

6.2.2 Sub-domain

381

(1)

6.2.3 Least Squares

381

(1)

6.2.4 Galerkin

381

(3)

6.3 Rayleigh-Ritz Method

384

(7)

6.3.1 Boundary Conditions and Continuity Requirements in Rayleigh-Ritz

385

(1)

6.3.2 Rayleigh-Ritz versus Galerkin

386

(1)

6.3.3 Rayleigh-Ritz versus Finite Elements

387

(1)

6.3.4 Rayleigh-Ritz Method for Discrete Systems

388

(2)

6.3.5 Trial Functions versus True Modes

390

(1)

6.4 Discrete Systems via Lagrange's Equations

391

(9)

6.4.1 Assumed Modes Method

391

(1)

6.4.2 Partial Derivatives

391

(1)

6.4.3 Examples of Application

392

(7)

6.4.4 What If Some of the Discrete Equations Remain Uncoupled?

399

(1)

6.5 Numerical Integration in the Time Domain

400

(17)

6.5.1 Physical Approximations to the Forcing Function

401

(2)

6.5.2 Physical Approximations to the Response

403

(3)

Constant Acceleration Method

403

(1)

Linear Acceleration Method

404

(1)

Newmark's beta Method

404

(1)

Impulse Acceleration Method

405

(1)

6.5.3 Methods Based on Mathematical Approximations

406

(4)

Multistep Methods for First-Order Differential Equations

407

(2)

Difference and Integration Formulas

409

(1)

Multistep Methods for Second-Order Differential Equations

409

(1)

6.5.4 Runge-Kutta Type Methods

410

(3)

Euler's Method

411

(1)

Improved and Modified Euler Methods

411

(1)

The Normal Runge-Kutta Method

412

(1)

6.5.5 Stability and Convergence Conditions for Multistep Methods

413

(3)

Conditional and Unconditional Stability of Linear Systems

413

(3)

6.5.6 Stability Considerations for Implicit Integration Schemes

416

(1)

6.6 Fundamentals of Fourier Methods

417

(23)

6.6.1 Fourier Transform

417

(3)

6.6.2 Fourier Series

420

(2)

6.6.3 Discrete Fourier Transform

422

(1)

6.6.4 Discrete Fourier Series

423

(3)

6.6.5 The Fast Fourier Transform

426

(1)

6.6.6 Orthogonality Properties of Fourier Expansions

427

(1)

a Fourier Transform

427

(1)

b Fourier Series

427

(1)

c Discrete Fourier Series

427

(1)

6.6.7 Fourier Series Representation of a Train of Periodic Impulses

428

(1)

6.6.8 Wraparound, Folding, and Aliasing

428

(2)

6.6.9 Trigonometric Interpolation and the Fundamental Sampling Theorem

430

(2)

6.6.10 Smoothing, Filtering, Truncation, and Data Decimation

432

(1)

6.6.11 Mean Value

432

(1)

6.6.12 Parseval's Theorem

433

(1)

6.6.13 Summary of Important Points

434

(1)

6.6.14 Frequency Domain Analysis of Lightly Damped or Undamped Systems

434

(6)

Exponential Window Method: The Preferred Tool

435

(5)

6.7 Fundamentals of Finite Elements

440

(41)

6.7.1 Gaussian Quadrature

441

(3)

Normalization

442

(2)

6.7.2 Integration in the Plane

444

(7)

a Integral over a Rectangular Area

446

(1)

b Integral over a Triangular Area

447

(1)

c Curvilinear Triangle

448

(2)

d Quadrilateral

450

(1)

e Curvilinear Quadrilateral

451

(1)

Inadmissible Shapes

451

(1)

6.7.3 Finite Elements via Principle of Virtual Displacements

451

(4)

a Consistency

454

(1)

b Conformity

454

(1)

c Rigid Body Test

454

(1)

d Convergence (Patch Test)

454

(1)

6.7.4 Plate Stretching Elements (Plane Strain)

455

(4)

a Triangular Element

455

(2)

b Rectangular Element

457

(2)

6.7.5 Isoparametric Elements

459

(22)

Plane Strain Curvilinear Quadrilaterals

459

(4)

Cylindrical Coordinates

463

(18)

7 Earthquake Engineering and Soil Dynamics

481

(84)

7.1 Stochastic Processes in Soil Dynamics

481

(13)

7.1.1 Expectations of a Random Process

481

(1)

7.1.2 Functions of Random Variable

482

(1)

7.1.3 Stationary Processes

482

(1)

7.1.4 Ergodic Processes

483

(1)

7.1.5 Spectral Density Functions

483

(1)

7.1.6 Coherence Function

484

(1)

7.1.7 Estimation of Spectral Properties

484

(4)

7.1.8 Spatial Coherence of Seismic Motions

488

(6)

Coherency Function Based on Statistical Analyses of Actual Earthquake Motions

488

(2)

Wave Model for Random Field

490

(1)

Simple Cross-Spectrum for SH Waves

490

(3)

Stochastic Deconvolution

493

(1)

7.2 Earthquakes, and Measures of Quake Strength

494

(8)

7.2.1 Magnitude

495

(2)

Seismic Moment

495

(2)

Moment Magnitude

497

(1)

7.2.2 Seismic Intensity

497

(2)

7.2.3 Seismic Risk: Gutenberg-Richter Law

499

(1)

7.2.4 Direction of Intense Shaking

500

(2)

7.3 Ground Response Spectra

502

(11)

7.3.1 Preliminary Concepts

502

(2)

7.3.2 Tripartite Response Spectrum

504

(1)

7.3.3 Design Spectra

505

(1)

7.3.4 Design Spectrum in the style of ASCE/SEI-7-05

506

(1)

Design Earthquake

506

(1)

Transition Periods

506

(1)

Implied Ground Motion Parameters

507

(1)

7.3.5 MDOF Systems: Estimating Maximum Values from Response Spectra

507

(6)

Common Error in Modal Combination

510

(1)

General Case: Response Spectrum Estimation for Complete Seismic Environment

511

(2)

7.4 Dynamic Soil-Structure Interaction

513

(38)

7.4.1 General Considerations

513

(2)

Seismic Excitation (Free-Field Problem)

514

(1)

Kinematic Interaction

514

(1)

Inertial Interaction

515

(1)

7.4.2 Modeling Considerations

515

(2)

Continuum Solutions versus Finite Elements

515

(1)

Finite Element Discretization

515

(1)

Boundary Conditions

516

(1)

7.4.3 Solution Methods

517

(5)

Direct Approach

517

(1)

Superposition Theorem

518

(1)

Three-Step Approach

519

(1)

Approximate Stiffness Functions

520

(2)

7.4.4 Direct Formulation of SSI Problems

522

(4)

The Substructure Theorem

522

(2)

SSI Equations for Structures with Rigid Foundation

524

(2)

7.4.5 SSI via Modal Synthesis in the Frequency Domain

526

(8)

Partial Modal Summation

529

(2)

What If the Modes Occupy Only a Subspace?

531

(2)

Member Forces

533

(1)

7.4.6 The Free-Field Problem: Elements of 1-D Soil Amplification

534

(6)

Effect of Location of Control Motion in 1-D Soil Amplification

537

(3)

7.4.7 Kinematic Interaction of Rigid Foundations

540

(11)

Iguchi's Approximation, General Case

541

(3)

Iguchi Approximation for Cylindrical Foundations Subjected to SH Waves

544

(1)

Geometric Properties

545

(1)

Free-Field Motion Components at Arbitrary Point, Zero Azimuth

546

(1)

Surface Integrals

546

(2)

Volume Integrals

548

(1)

Effective Motions

549

(2)

7.5 Simple Models for Time-Varying, Inelastic Soil Behavior

551

(10)

7.5.1 Inelastic Material Subjected to Cyclic Loads

551

(2)

7.5.2 Masing's Rule

553

(2)

7.5.3 Ivan's Model: Set of Elastoplastic Springs in Parallel

555

(1)

7.5.4 Hyperbolic Model

556

(2)

7.5.5 Ramberg-Osgood Model

558

(3)

7.6 Response of Soil Deposits to Blast Loads

561

(4)

7.6.1 Effects of Ground-Borne Blast Vibrations on Structures

561

(4)

Frequency Effects

561

(1)

Distance Effects

562

(1)

Structural Damage

563

(2)

8 Advanced Topics

565

(54)

8.1 The Hilbert Transform

565

(8)

8.1.1 Definition

565

(1)

8.1.2 Fourier Transform of the Sign Function

566

(1)

8.1.3 Properties of the Hilbert Transform

567

(2)

8.1.4 Causal Functions

569

(1)

8.1.5 Kramers-Kronig Dispersion Relations

570

(3)

Minimum Phase Systems

572

(1)

Time-Shifted Causality

573

(1)

8.2 Transfer Functions, Normal Modes, and Residues

573

(7)

8.2.1 Poles and Zeros

573

(1)

8.2.2 Special Case: No Damping

574

(1)

8.2.3 Amplitude and Phase of the Transfer Function

575

(5)

8.2.4 Normal Modes versus Residues

8.3 Correspondence Principle

580

(2)

8.4 Numerical Correspondence of Damped and Undamped Solutions

582

(3)

8.4.1 Numerical Quadrature Method

582

(2)

8.4.2 Perturbation Method

584

(1)

8.5 Gyroscopic Forces Due to Rotor Support Motions

585

(5)

8.6 Rotationally Periodic Structures

590

(6)

8.6.1 Structures Composed of Identical Units and with Polar Symmetry

590

(3)

8.6.2 Basic Properties of Block-Circulant Matrices

593

(1)

8.6.3 Dynamics of Rotationally Periodic Structures

594

(2)

8.7 Spatially Periodic Structures

596

(14)

8.7.1 Method 1: Solution in Terms of Transfer Matrices

596

(6)

8.7.2 Method 2: Solution via Static Condensation and Cloning

602

(2)

Example: Waves in a Thick Solid Rod Subjected to Dynamic Source

603

(1)

8.7.3 Method 3: Solution via Wave Propagation Modes

604

(6)

Example 1: Set of Identical Masses Hanging from a Taut String

605

(3)

Example 2: Infinite Chain of Viscoelastically Supported Masses and Spring-Dashpots

608

(2)

8.8 The Discrete Shear Beam

610

(9)

8.8.1 Continuous Shear Beam

611

(1)

8.8.2 Discrete Shear Beam

611

(8)

9 Mathematical Tools

619

(28)

9.1 Dirac Delta and Related Singularity Functions

619

(2)

9.1.1 Related Singularity Functions

620

(6)

Doublet Function

620

(1)

Dirac Delta Function

620

(1)

Unit Step Function (Heaviside Function)

620

(1)

Unit Ramp Function

621

(1)

9.2 Functions of Complex Variables: A Brief Summary

621

(5)

9.3 Wavelets

626

(4)

9.3.1 Box Function

626

(1)

9.3.2 Hanning Bell (or Window)

626

(1)

9.3.3 Gaussian Bell

627

(1)

9.3.4 Modulated Sine Pulse (Antisymmetric Bell)

628

(1)

9.3.5 Ricker Wavelet

628

(2)

9.4 Useful Integrals Involving Exponentials

630

(1)

9.4.1 Special Cases

630

(1)

9.5 Integration Theorems in Two and Three Dimensions

630

(3)

9.5.1 Integration by Parts

631

(1)

9.5.2 Integration Theorems

631

(2)

9.5.3 Particular Cases: Gauss, Stokes, and Green

633

(1)

9.6 Positive Definiteness of Arbitrary Square Matrix

633

(7)

9.7 Derivative of Matrix Determinant: The Trace Theorem

640

(2)

9.8 Circulant and Block-Circulant Matrices

642

(5)

9.8.1 Circulant Matrices

642

(2)

9.8.2 Block-Circulant Matrices

644

(3)

10 Problem Sets

647

(66)

Author Index

713

(1)

Subject Index

714

Professor Eduardo Kausel is a specialist in structural dynamics in the Department of Civil and Environmental Engineering at the Massachusetts Institute of Technology (MIT). He is especially well known for two papers on the collapse of the Twin Towers on September 11, 2001. The first of this pair, published on MIT's website only a few days after the terrorist act, attracted more readers around the world than all other works and publications on the subject combined. Kausel is the author of Fundamental Solutions in Elastodynamics: A Compendium (Cambridge, 2011).

Advanced Structural Dynamics [Kõva köide]

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