Vibration Theory and Applications with Finite Elements and Active Vibration Control

1. Auflage 2016
ISBN: 978-1-118-35080-5
Verlag: Wiley

Buch, Englisch, 976 Seiten, Format (B × H): 187 mm x 260 mm, Gewicht: 1721 g

Based on many years of research and teaching, this book brings together all the important topics in linear vibration theory, including failure models, kinematics and modeling, unstable vibrating systems, rotordynamics, model reduction methods, and finite element methods utilizing truss, beam, membrane and solid elements. It also explores in detail active vibration control, instability and modal analysis. The book provides the modeling skills and knowledge required for modern engineering practice, plus the tools needed to identify, formulate and solve engineering problems effectively.

Autoren/Hrsg.

Palazzolo, Alan B

Palazzolo, Alan

Fachgebiete

• Technische Wissenschaften Bauingenieurwesen Technische Dynamik (Modalanalyse), Erdbebensicherheit
• Technische Wissenschaften Bauingenieurwesen Konstruktiver Ingenieurbau, Baustatik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik

Inhaltsverzeichnis

Preface xv

Acknowledgments and Dedication xxi

About the Companion Website xxiii

List of Acronyms xxv

1 Background, Motivation, and Overview 1

1.1 Introduction 1

1.2 Background 1

1.2.1 Units 5

1.3 Our Vibrating World 6

1.3.1 Small-Scale Vibrations 6

1.3.2 Medium-Scale (Mesoscale) Vibrations 8

1.3.3 Large-Scale Vibrations 8

1.4 Harmful Effects of Vibration 9

1.4.1 Human Exposure Limits 9

1.4.2 High-Cycle Fatigue Failure 11

1.4.3 Rotating Machinery Vibration 21

1.4.4 Machinery Productivity 27

1.4.5 Fastener Looseness 28

1.4.6 Optical Instrument Blurring 28

1.4.7 Ethics and Professional Responsibility 29

1.4.8 Lifelong Learning Opportunities 29

1.5 Stiffness, Inertia, and Damping Forces 29

1.6 Approaches for Obtaining the Differential Equations of Motion 34

1.7 Finite Element Method 35

1.8 Active Vibration Control 37

1.9 Chapter 1 Exercises 37

1.9.1 Exercise Location 37

1.9.2 Exercise Goals 37

1.9.3 Sample Exercises: 1.6 and 1.11 38

References 38

2 Preparatory Skills: Mathematics, Modeling, and Kinematics 41

2.1 Introduction 41

2.2 Getting Started with MATLAB and MAPLE 42

2.2.1 MATLAB 42

2.2.2 MAPLE (Symbolic Math) 45

2.3 Vibration and Differential Equations 50

2.3.1 MATLAB and MAPLE Integration 50

2.4 Taylor Series Expansions and Linearization 56

2.5 Complex Variables (CV) and Phasors 60

2.6 Degrees of Freedom, Matrices, Vectors, and Subspaces 63

2.6.1 Matrix–Vector Related Definitions and Identities 69

2.7 Coordinate Transformations 75

2.8 Eigenvalues and Eigenvectors 79

2.9 Fourier Series 80

2.10 Laplace Transforms, Transfer Functions, and Characteristic Equations 83

2.11 Kinematics and Kinematic Constraints 86

2.11.1 Particle Kinematic Constraint 86

2.11.2 Rigid Body Kinematic Constraint 90

2.11.3 Assumed Modes Kinematic Constraint 96

2.11.4 Finite Element Kinematic Constraint 98

2.12 Dirac Delta and Heaviside Functions 100

2.13 Chapter 2 Exercises 101

2.13.1 Exercise Location 101

2.13.2 Exercise Goals 101

2.13.3 Sample Exercises: 2.9 and 2.17 101

References 102

3 Equations of Motion by Newton’s Laws 103

3.1 Introduction 103

3.2 Particle Motion Approximation 103

3.3 Planar (2D) Rigid Body Motion Approximation 107

3.3.1 Translational Equations of Motion 107

3.3.2 Rotational Equation of Motion 108

3.4 Impulse and Momentum 129

3.4.1 Linear Impulse and Momentum 129

3.4.2 Angular Impulse and Momentum 134

3.5 Variable Mass Systems 138

3.6 Chapter 3 Exercises 140

3.6.1 Exercise Location 140

3.6.2 Exercise Goals 140

3.6.3 Sample Exercises: 3.8 and 3.21 141

References 141

4 Equations of Motion by Energy Methods 143

4.1 Introduction 143

4.2 Kinetic Energy 143

4.2.1 Particle Motion 143

4.2.2 Two-Dimensional Rigid Body Motion 144

4.2.3 Constrained 2D Rigid Body Motion 146

4.3 External and Internal Work and Potential Energy 147

4.3.1 External Work and Potential Energy 150

4.4 Power and Work–Energy Laws 151

4.4.1 Particles 151

4.4.2 Rigid Body with 2D Motion 153

4.5 Lagrange Equation for Particles and Rigid Bodies 157

4.5.1 Derivation of the Lagrange Equation 158

4.5.2 System of Particles 160

4.5.3 Collection of Rigid Bodies 162

4.5.4 Potential, Circulation, and Dissipation Functions 168

4.5.5 Summary for Lagrange Equation 182

4.5.6 Nonconservative Generalized Forces and Virtual Work 183

4.5.7 Effects of Gravity for the Lagrange Approach 195

4.5.8 “Automating” the Derivation of the LE Approach 201

4.6 LE for Flexible, Distributed Mass Bodies: Assumed Modes Approach 211

4.6.1 Assumed Modes Kinetic Energy and Mass Matrix Expressions 212

4.6.2 Rotating Structures 215

4.6.3 Internal Forces and Strain Energy of an Elastic Object 216

4.6.4 The Assumed Modes Approximation 219

4.6.5 Generalized Force for External Loads Acting on a Deformable Body 221

4.6.6 Assumed Modes Model Generalized Forces for External Load Acting on a Deformable Body 221

4.6.7 LE for a System of Rigid and Deformable Bodies 223

4.7 LE for Flexible, Distributed Mass Bodies: Finite Element Approach—General Formulation 267

4.7.1 Element Kinetic Energy and Mass Matrix 267

4.7.2 Element Stiffness Matrix 269

4.7.3 Summary 272

4.8 LE for Flexible, Distributed Mass Bodies: Finite Element Approach—Bar/Truss Modes 275

4.8.1 Introduction 275

4.8.2 1D Truss/Bar Element 276

4.8.3 1D Truss/Bar Element: Element Stiffness Matrix 276

4.8.4 1D Truss/Bar Element: Element Mass Matrix 277

4.8.5 1D Truss/Bar Element: Element Damping Matrix 277

4.8.6 1D Truss/Bar Element: Generalized Force Vector 278

4.8.7 1D Truss/Bar Element: Nodal Connectivity Array 279

4.8.8 System of 1D Bar Elements: Matrix Assembly 280

4.8.9 Incorporation of Displacement Constraint 285

4.8.10 Modeling of 2D Trusses 289

4.8.11 2D Truss/Bar Element: Element Stiffness Matrix 292

4.8.12 2D Truss/Bar Element: Element Mass Matrix 293

4.8.13 2D Truss/Bar Element: Element Damping Matrix 294

4.8.14 2D Truss/Bar Element: Element Force Vector 295

4.8.15 2D Truss/Bar Element: Element Action Vector 296

4.8.16 2D Truss/Bar Element: Degree of Freedom Connectivity Array and Matrix Assembly 296

4.8.17 2D Truss/Bar Element: Rigid Region Modeling for 2D Trusses 303

4.9 Chapter 4 Exercises 306

4.9.1 Exercise Location 306

4.9.2 Exercise Goals 307

4.9.3 Sample Exercises: 4.43 and 4.52 307

References 308

5 Free Vibration Response 309

5.1 Introduction 309

5.2 Single Degree of Freedom Systems 309

5.2.1 SDOF Eigenvalues (Characteristic Roots) 310

5.2.2 SDOF Initial Condition Response 311

5.2.3 Log Decrement: A Measure of Damping—Displacement-Based Measurement 313

5.2.4 Log Decrement: A Measure of Damping—Acceleration-Based Measurement 315

5.3 Two-Degree-of-Freedom Systems 319

5.3.1 Special Case I (C=G=KC = 0) (Undamped, Nongyroscopic, and Noncirculatory Case) 322

5.3.2 Special Case IIC=KC = 0 (Undamped, Gyroscopic, and Noncirculatory Case) 332

5.3.3 Special Case III C=G=0 (Undamped, Nongyroscopic, and Circulatory Case) 342

5.4 N-Degree-of-Freedom Systems 346

5.4.1 General Identities 346

5.4.2 Undamped, Nongyroscopic, and Noncirculatory Systems—Description 346

5.4.3 Undamped, Nongyroscopic, and Noncirculatory Systems—Solution Form 347

5.4.4 Undamped, Nongyroscopic, and Noncirculatory Systems—Orthogonality 349

5.4.5 Undamped, Nongyroscopic, and Noncirculatory Systems—IC Response 351

5.4.6 Undamped, Nongyroscopic, and Noncirculatory Systems—Rigid Body Modes 352

5.4.7 Summary 353

5.4.8 Undamped, Nongyroscopic, and Noncirculatory Systems—Response to an IC Modal Displacement Distribution 363

5.4.9 Orthogonally Damped, Nongyroscopic, and Noncirculatory Systems—Description 364

5.4.10 Orthogonally Damped, Nongyroscopic, and Noncirculatory Systems—Eigenvalues and Eigenvectors 365

5.4.11 Orthogonally Damped, Nongyroscopic, and Noncirculatory Systems—IC Response 366

5.4.12 Orthogonally Damped, Nongyroscopic, and Noncirculatory Systems—Determination of C0 367

5.4.13 Nonorthogonally Damped System with Symmetric Mass, Stiffness, and Damping Matrices 377

5.4.14 Undamped, Gyroscopic, and Noncirculatory Systems—Description 379

5.4.15 Undamped, Gyroscopic, and Noncirculatory Systems—Eigenvalues and Eigenvectors 380

5.4.16 Undamped, Gyroscopic, and Noncirculatory Systems—Biorthogonality 385

5.4.17 General Linear Systems—Description 388

5.4.18 General Linear Systems—Biorthogonality 389

5.5 Infinite Dof Continuous Member Systems 390

5.5.1 Introduction 390

5.5.2 Transverse Vibration of Strings and Cables 390

5.5.3 Axial Vibration of a Uniform Bar 394

5.5.4 Torsion of Bars 396

5.5.5 Euler–Bernoulli (Classical) Beam Theory 400

5.5.6 Timoshenko Beam Theory 404

5.6 Unstable Free Vibrations 408

5.6.1 Oil Film Bearing-Induced Instability 411

5.7 Summary 418

5.8 Chapter 5 Exercises 418

5.8.1 Exercise Location 418

5.8.2 Exercise Goals 418

5.8.3 Sample Exercises: 5.25 and 5.35 419

References 419

6 Vibration Response Due to Transient Loading 421

6.1 Introduction 421

6.2 Single Degree of Freedom Transient Response 421

6.2.1 Direct Analytical Solution Method 422

6.2.2 Laplace Transform Method 428

6.2.3 Convolution Integral 434

6.2.4 Response to Successive Disturbances 438

6.2.5 Pulsed Excitations 440

6.2.6 Response Spectrum 444

6.3 Modal Condensation of Ndof: Transient Forced Vibrating Systems 451

6.3.1 Undamped and Orthogonally Damped Nongyroscopic, Noncirculatory Systems 452

6.3.2 Unconstrained Structures 465

6.3.3 Base Excitation 475

6.3.4 Participation Factor and Modal Effective Mass 477

6.3.5 General Nonsymmetric, Nonorthogonal Damping Models 488

6.4 Numerical Integration of Ndof Transient Vibration Response 493

6.4.1 Second-Order System NI Algorithms 494

6.4.2 First-Order System NI Algorithms 500

6.5 Summary 521

6.6 Chapter 6 Exercises 522

6.6.1 Exercise Location 522

6.6.2 Exercise Goals 522

6.6.3 Sample Exercises: 6.18 and 6.21 522

References 523

7 Steady-State Vibration Response to Periodic Loading 525

7.1 Introduction 525

7.2 Complex Phasor Approach 525

7.3 Single Degree of Freedom Mo

Über Autor(innen)

Alan Palazzolo, Professor of Mechanical Engineering, Texas A&M University. Professor Palazzolo worked in industry prior to returning to academic research and gaining full Professorship in Mechanical Engineering in 1999.?He has written extensively for international journals, books and conference proceedings and has been the recipient of numerous awards throughout his professional career. His research interests include vibrations, nonlinear vibrations, controls, rotordynamics and finite elements. He is presently an Associate Editor of ASME Journal of Vibrations.