Singiresu S. Rao

Vibration of Continuous Systems (eBook, ePUB)

• Format: ePub

Produktbeschreibung

A revised and up-to-date guide to advanced vibration analysis written by a noted expert The revised and updated second edition of Vibration of Continuous Systems offers a guide to all aspects of vibration of continuous systems including: derivation of equations of motion, exact and approximate solutions and computational aspects. The author--a noted expert in the field--reviews all possible types of continuous structural members and systems including strings, shafts, beams, membranes, plates, shells, three-dimensional bodies, and composite structural members. Designed to be a useful aid in the understanding of the vibration of continuous systems, the book contains exact analytical solutions, approximate analytical solutions, and numerical solutions. All the methods are presented in clear and simple terms and the second edition offers a more detailed explanation of the fundamentals and basic concepts. Vibration of Continuous Systems revised second edition: * Contains new chapters on Vibration of three-dimensional solid bodies; Vibration of composite structures; and Numerical solution using the finite element method * Reviews the fundamental concepts in clear and concise language * Includes newly formatted content that is streamlined for effectiveness * Offers many new illustrative examples and problems * Presents answers to selected problems Written for professors, students of mechanics of vibration courses, and researchers, the revised second edition of Vibration of Continuous Systems offers an authoritative guide filled with illustrative examples of the theory, computational details, and applications of vibration of continuous systems.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 816
• Erscheinungstermin: 24. Januar 2019
• Englisch
• ISBN-13: 9781119424277
• Artikelnr.: 55075471

Autorenporträt

Singiresu S. Rao is a Professor in the Mechanical and Aerospace Engineering Department at the University of Miami. His main areas of research include structural dynamics, multi objective optimization and development of uncertainty models in engineering modeling, analysis, design and optimization. He is a Fellow of ASME and an Associate Fellow of the AIAA.

Inhaltsangabe

Preface xv

Acknowledgments xix

About the Author xxi

1 Introduction: Basic Concepts and Terminology 1

1.1 Concept of Vibration 1

1.2 Importance of Vibration 4

1.3 Origins and Developments in Mechanics and Vibration 5

1.4 History of Vibration of Continuous Systems 7

1.5 Discrete and Continuous Systems 12

1.6 Vibration Problems 15

1.7 Vibration Analysis 16

1.8 Excitations 17

1.9 Harmonic Functions 17

1.10 Periodic Functions and Fourier Series 24

1.11 Non periodic Functions and Fourier Integrals 25

1.12 Literature on Vibration of Continuous Systems 28

References 29

Problems 31

2 Vibration of Discrete Systems: Brief Review 33

2.1 Vibration of a Single-Degree-of-Freedom System 33

2.2 Vibration of Multi degree-of-Freedom Systems 43

2.3 Recent Contributions 60

References 61

Problems 62

3 Derivation of Equations: Equilibrium Approach 69

3.1 Introduction 69

3.2 Newton's Second Law of Motion 69

3.3 D'Alembert's Principle 70

3.4 Equation of Motion of a Bar in Axial Vibration 70

3.5 Equation of Motion of a Beam in Transverse Vibration 72

3.6 Equation of Motion of a Plate in Transverse Vibration 74

3.7 Additional Contributions 81

References 81

Problems 82

4 Derivation of Equations: Variational Approach 87

4.1 Introduction 87

4.2 Calculus of a Single Variable 87

4.3 Calculus of Variations 88

4.4 Variation Operator 91

4.5 Functional with Higher-Order Derivatives 93

4.6 Functional with Several Dependent Variables 95

4.7 Functional with Several Independent Variables 96

4.8 Extremization of a Functional with Constraints 98

4.9 Boundary Conditions 102

4.10 Variational Methods in Solid Mechanics 106

4.11 Applications of Hamilton's Principle 116

4.12 Recent Contributions 121

Notes 121

References 122

Problems 122

5 Derivation of Equations: Integral Equation Approach 125

5.1 Introduction 125

5.2 Classification of Integral Equations 125

5.3 Derivation of Integral Equations 127

5.4 General Formulation of the Eigenvalue Problem 132

5.6 Recent Contributions 149

References 150

Problems 151

6 Solution Procedure: Eigenvalue and Modal Analysis Approach 153

6.1 Introduction 153

6.2 General Problem 153

6.3 Solution of Homogeneous Equations: Separation-of-Variables Technique 155

6.4 Sturm-Liouville Problem 156

6.5 General Eigenvalue Problem 165

6.6 Solution of Nonhomogeneous Equations 169

6.7 Forced Response of Viscously Damped Systems 171

6.8 Recent Contributions 173

References 174

Problems 175

7 Solution Procedure: Integral Transform Methods 177

7.1 Introduction 177

7.2 Fourier Transforms 178

7.3 Free Vibration of a Finite String 184

7.4 Forced Vibration of a Finite String 186

7.5 Free Vibration of a Beam 188

7.6 Laplace Transforms 191

7.7 Free Vibration of a String of Finite Length 197

7.8 Free Vibration of a Beam of Finite Length 200

7.9 Forced Vibration of a Beam of Finite Length 201

7.10 Recent Contributions 204

References 205

Problems 206

8 Transverse Vibration of Strings 209

8.1 Introduction 209