Linear and nonlinear structural mechanics / Ali H. Nayfeh, P. Frank Pai.

Format:

Book

Author/Creator:

Nayfeh, Ali Hasan, 1933-

Contributor:

Pai, P. Frank (Perngjin Frank)

Engineering Book Fund.

Series:

Wiley series in nonlinear science

Language:

English

Subjects (All):

Structural analysis (Engineering).

Nonlinear mechanics.

Elastic analysis (Engineering).

Physical Description:

xvii, 746 pages : illustrations ; 25 cm.

Place of Publication:

Hoboken, N.J. : Wiley-Interscience, [2004]

Summary:

* Explains the physical meaning of linear and nonlinear structural mechanics. * Shows how to perform nonlinear structural analysis. * Points out important nonlinear structural dynamics behaviors. * Provides ready-to-use governing equations.

Contents:

1.1 Structural Elements 1

1.2 Nonlinearities 4

1.3 Composite Materials 6

1.4 Damping 7

1.5 Dynamic Characteristics of Linear Discrete Systems 9

1.5.1 One-Degree-of-Freedom Systems 9

1.5.2 Multi-Degree-of-Freedom Systems 14

1.6 Dynamic Characteristics of Nonlinear Discrete Systems 22

1.7 Analyses of Linear Continuous Systems 27

1.7.1 Natural Frequencies and Eigenfunctions 30

1.7.2 Discretization Using Eigenfunctions 34

1.7.3 The Ritz Method 35

1.7.4 Finite Element Method 42

1.7.5 Weighted Residual Methods 46

1.7.6 Initial-Value Methods 48

1.8 Analyses of Nonlinear Continuous Systems 53

1.8.1 Attacking the Continuous System 57

1.8.2 Attacking the Discretized System 60

1.8.3 Time-Averaged Lagrangian 63

2 Elasticity 65

2.1 Principles of Dynamics 65

2.1.1 Newton's Second Law and Energy of a Discrete System 67

2.1.2 Principle of Virtual Work 69

2.1.3 Hamilton's Theories 70

2.1.4 Euler-Lagrange Equations 72

2.1.5 Hamilton's Equations 74

2.2 Strain-Displacement Relations 75

2.3 Transformation of Strains and Stresses 82

2.4 Stress-Strain Relations 85

2.4.1 Anisotropic Materials 86

2.4.2 Orthotropic Materials 87

2.4.3 Isotropic Materials 90

2.4.4 Material Stiffness and Compliance Matrices 94

2.4.5 Fiber-Reinforced Lamina 96

2.5 Governing Equations 98

2.5.1 Equilibrium Equations 99

2.5.2 Compatibility Conditions 107

2.5.3 Energy Formulation of Structures 109

3 Strings and Cables 111

3.1 Modeling of Taut Strings 111

3.1.1 Exact Equations of Motion 113

3.1.2 Approximate Equations of Motion without Poisson's Effect 115

3.1.3 Approximate Equations of Motion with Poisson's Effect 117

3.2 Reduction of String Model to Two Equations 118

3.2.1 Attacking the Three-Equation Model 121

3.2.2 Evaluation of the Two-Equation Model 124

3.2.3 Discretized Model 126

3.3 Nonlinear Response of Strings 129

3.3.1 Frequency-Response Curves 130

3.3.2 Experiments 132

3.4 Modeling of Cables 136

3.4.1 Exact Equations of Motion 139

3.4.2 Static Deflections 141

3.4.3 Approximate Equations of Motion 145

3.5 Reduction of Cable Model to Two Equations 146

3.6 Natural Frequencies and Modes of Cables 148

3.7 Discretization of the Cable Equations 150

3.8 Single-Mode Response with Direct Approach 152

3.8.1 Primary Resonance of an Inplane Mode 153

3.8.2 Primary Resonance of an out-of-Plane Mode 158

3.9 Single-Mode Response with Discretization Approach 161

3.9.1 The Case of an Inplane Mode 162

3.9.2 The Case of an out-of-Plane Mode 167

3.10 Extensional Bars 168

4 Beams 171

4.1.1 Beam Theories 172

4.1.2 Geometric Nonlinearities 176

4.1.3 Shear Deformations, Rotary Inertias, and Gravity 179

4.1.4 Elastic Couplings 180

4.1.5 External and Internal Resonances 180

4.2 Linear Euler-Bernoulli Beam Theory 183

4.3 Linear Shear-Deformable Beam Theories 186

4.3.1 Third-Order Shear-Deformable Theory 189

4.3.2 Timoshenko's Beam Theory 191

4.3.3 Layerwise Shear-Deformable Theory 192

4.4 Mathematics for Nonlinear Modeling 194

4.4.1 Coordinate Transformations and Curvatures 194

4.4.2 Concept of Orthogonal Virtual Rotations 207

4.4.3 Variation of Curvatures 210

4.4.4 Concept of Local Displacements 211

4.5 Nonlinear 2-D Euler-Bernoulli Beam Theory 215

4.5.1 Shortening Effect 221

4.5.2 Stretching Effect 224

4.5.3 Lagrangian and Eulerian Coordinates 225

4.6 Nonlinear 3-D Euler-Bernoulli Beam Theory 226

4.6.1 Isotropic Beams 234

4.6.2 Composite Beams 235

4.6.3 Taylor-Series Expansions 235

4.6.4 Cantilevered Inextensional Beams 240

4.6.5 Flexural-Flexural Vibration 244

4.7 Nonlinear 3-D Curved Beam Theory Accounting for Warpings 245

4.7.1 Inplane and out-of-Plane Warpings 247

4.7.2 Fully Nonlinear Jaumann Strains 251

4.7.3 Equations of Motion 254

4.7.4 Expansions and Simplified Beam Theories 262

4.7.5 Applications 263

5 Dynamics of Beams 267

5.1 Parametrically Excited Cantilever Beams 267

5.1.1 Experiments 267

5.1.2 Principal Parametric Resonance 270

5.1.3 Combination Parametric Resonance 278

5.1.4 Nonplanar Dynamics 284

5.2 Transversely Excited Cantilever Beams 291

5.2.1 Planar Response to a Primary-Resonance Excitation 291

5.2.2 External Subcombination Resonance 298

5.2.3 Nonplanar Dynamics 304

5.3 Clamped-Clamped Buckled Beams 316

5.3.1 Buckling Problem 320

5.3.2 Linear Vibration Problem 321

5.3.3 Nonlinear Local Vibrations - Direct Approach 324

5.3.4 Nonlinear Local Vibrations - Discretization Approach 327

5.3.5 Experiment 331

5.3.6 Global Dynamics 334

5.4 Microbeams 341

5.4.1 Modeling of MEMS Devices 342

5.4.2 Static Deflection 344

5.4.3 Linear Mode Shapes and Frequencies 345

5.4.4 Nonlinear Response to a Primary-Resonance Excitation 346

5.4.5 Reduced-Order Models of MEMS Devices 351

6 Surface Analysis 355

6.1 Initial Curvatures 355

6.2 Inplane Strains and Deformed Curvatures 358

6.3 Orthogonal Virtual Rotations 362

6.3.1 Without Inplane Shear Strains 362

6.3.2 With Inplane Shear Strains 363

6.4 Variation of Curvatures 365

6.5 Local Displacements and Jaumann Strains 366

7 Plates 371

7.1.1 Plate Theories 371

7.1.2 Geometric Nonlinearities 375

7.1.3 Plates with Integrated Piezoelectric Materials 376

7.1.4 Linear Vibrations and Buckling of Plates 377

7.1.5 Nonlinear Analyses of Plates 379

7.2 Linear Classical Plate Theory 382

7.2.1 Rectangular Plates 382

7.2.2 Circular Plates 388

7.2.3 General Plates 392

7.3 Linear Shear-Deformable Plate Theories 396

7.3.1 Formulation for Curvilinear Coordinate Systems 396

7.3.2 Rectangular and Circular Plates 401

7.3.3 Different Shear-Warping Functions 402

7.4 Nonlinear Classical Plate Theory 403

7.4.1 Rectangular Plates 403

7.4.2 von Karman Plate Theory in Polar Coordinates 408

7.4.3 Thermoelastic Equations in Cartesian Coordinates 412

7.4.4 Thermoelastic Equations in Polar Coordinates 415

7.5 Nonlinear Modeling of Rectangular Surfaces 417

7.5.1 Coordinate Transformation, Inplane Strains, and Curvatures 417

7.5.2 Influence of the Inplane Shear Deformation 420

7.5.3 Variation of the Global Strains 425

7.6 General Nonlinear Classical Plate Theory 426

7.7 Nonlinear Shear-Deformable Plate Theory 435

7.7.1 Equations of Motion 436

7.7.2 Nonlinear First-Order Theory 446

7.7.3 Third-Order Theory with von Karman Nonlinearity 446

7.8 Nonlinear Layerwise Shear-Deformable Plate Theory 446

7.8.1 Warpings Due to External Loads and Actuators 447

7.8.2 Equations of Motion 457

7.8.3 Linear Piezoelectric Plate Theory 465

7.8.4 Actuator-Induced Loads 467

7.8.5 Thermal and Moisture Effects 467

8 Dynamics of Plates 469

8.1 Linear Vibrations of Rectangular Plates 469

8.1.1 Hinged Edges 470

8.1.2 Two Hinged Opposite Edges 470

8.2 Linear Vibrations of Membranes 474

8.2.1 Circular Membranes 474

8.2.2 Near Circular Membranes 477

8.2.3 Elliptic Membranes 480

8.3 Linear Vibrations of Circular and Annular Plates 481

8.3.1 Circular Plates 482

8.3.2 Near Circular and Elliptic Plates 487

8.3.3 Annular Plates 491

8.4 Nonlinear Vibrations of Circular Plates 498

8.4.1 Axisymmetric Vibrations 503

8.4.2 Asymmetric Vibrations 507

8.5 Nonlinear Vibrations of Rotating Disks 513

8.5.1 Static Problem 516

8.5.2 Natural Frequencies and Mode Shapes 517

8.5.3 Response to a Primary-Resonance Excitation 522

8.6 Nonlinear Vibrations of Near-Square Plates 527

8.7 Micropumps 531

8.7.1 Annular Plates 532

8.7.2 Circular Plates 536

8.8 Thermally Loaded Plates 543

8.8.1 Linear Natural Frequencies and Mode Shapes 548

8.8.2 Combination Parametric Resonance of Two Axisymmetric Modes 549

9 Shells 559

9.1.1 Shell

Theories 560

9.1.2 Nonlinear Vibrations of Shells 563

9.2 Linear Classical Shell Theory 566

9.2.1 Different Shell Geometries 566

9.2.2 Doubly-Curved Shell Theory 571

9.2.3 Circular Cylindrical Shell Theory 576

9.3 Linear Shear-Deformable Shell Theories 577

9.3.1 Formulation for General Shells 577

9.3.2 Equations of Motion for Different Shells 581

9.3.3 Shear-Warping Functions 581

9.4 Nonlinear Classical Theory for Doubly-Curved Shells 582

9.5 Nonlinear Shear-Deformable Theories for Circular Cylindrical Shells 588

9.5.1 Equations of Motion 589

9.5.2 Simplified Shell Theories 603

9.5.3 Stiffness Matrices 608

9.5.4 Classical Linear Theories of Circular Cylindrical Shells 611

9.6 Nonlinear Layerwise Shear-Deformable Shell Theory 615

9.6.1 Strains and Shear-Warping Functions 615

9.6.2 Inertia Terms 620

9.6.3 Structural Terms 622

9.6.4 Equations of Motion 625

9.6.5 Shear-Warping Functions 627

9.7 Nonlinear Dynamics of Infinitely Long Circular Cylindrical Shells 630

9.7.1 Governing Equations 631

9.7.2 Natural Frequencies and Mode Shapes 635

9.7.3 Primary Resonance of the Breathing Mode 638

9.8 Nonlinear Dynamics of Axisymmetric Motion of Closed Spherical Shells 641

9.8.1 Equations of Motion 641

9.8.2 Natural Frequencies and Mode Shapes 646

9.8.3 Two-to-One Internal Resonance 649.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Engineering Book Fund.

ISBN:

0471593567

OCLC:

52567246

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