Vibration of Continuous Systems, 2nd Edition

Vibration of Continuous Systems, 2nd Edition

by Singiresu S. Rao
Released March 2019
Publisher(s): Wiley
ISBN: 9781119424147

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Book description

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.

Table of contents

  1. Cover
  2. Preface
  3. Acknowledgments
  4. About the Author
  5. 1 Introduction: Basic Concepts and Terminology
    1. 1.1 CONCEPT OF VIBRATION
    2. 1.2 IMPORTANCE OF VIBRATION
    3. 1.3 ORIGINS AND DEVELOPMENTS IN MECHANICS AND VIBRATION
    4. 1.4 HISTORY OF VIBRATION OF CONTINUOUS SYSTEMS
    5. 1.5 DISCRETE AND CONTINUOUS SYSTEMS
    6. 1.6 VIBRATION PROBLEMS
    7. 1.7 VIBRATION ANALYSIS
    8. 1.8 EXCITATIONS
    9. 1.9 HARMONIC FUNCTIONS
    10. 1.10 PERIODIC FUNCTIONS AND FOURIER SERIES
    11. 1.11 NONPERIODIC FUNCTIONS AND FOURIER INTEGRALS
    12. 1.12 LITERATURE ON VIBRATION OF CONTINUOUS SYSTEMS
    13. REFERENCES
    14. PROBLEMS
  6. 2 Vibration of Discrete Systems: Brief Review
    1. 2.1 VIBRATION OF A SINGLE‐DEGREE‐OF‐FREEDOM SYSTEM
    2. 2.2 VIBRATION OF MULTIDEGREE‐OF‐FREEDOM SYSTEMS
    3. 2.3 RECENT CONTRIBUTIONS
    4. REFERENCES
    5. PROBLEMS
  7. 3 Derivation of Equations: Equilibrium Approach
    1. 3.1 INTRODUCTION
    2. 3.2 NEWTON'S SECOND LAW OF MOTION
    3. 3.3 D'ALEMBERT'S PRINCIPLE
    4. 3.4 EQUATION OF MOTION OF A BAR IN AXIAL VIBRATION
    5. 3.5 EQUATION OF MOTION OF A BEAM IN TRANSVERSE VIBRATION
    6. 3.6 EQUATION OF MOTION OF A PLATE IN TRANSVERSE VIBRATION
    7. 3.7 ADDITIONAL CONTRIBUTIONS
    8. REFERENCES
    9. PROBLEMS
  8. 4 Derivation of Equations: Variational Approach
    1. 4.1 INTRODUCTION
    2. 4.2 CALCULUS OF A SINGLE VARIABLE
    3. 4.3 CALCULUS OF VARIATIONS
    4. 4.4 VARIATION OPERATOR
    5. 4.5 FUNCTIONAL WITH HIGHER‐ORDER DERIVATIVES
    6. 4.6 FUNCTIONAL WITH SEVERAL DEPENDENT VARIABLES
    7. 4.7 FUNCTIONAL WITH SEVERAL INDEPENDENT VARIABLES
    8. 4.8 EXTREMIZATION OF A FUNCTIONAL WITH CONSTRAINTS
    9. 4.9 BOUNDARY CONDITIONS
    10. 4.10 VARIATIONAL METHODS IN SOLID MECHANICS
    11. 4.11 APPLICATIONS OF HAMILTON'S PRINCIPLE
    12. 4.12 RECENT CONTRIBUTIONS
    13. NOTES
    14. REFERENCES
    15. PROBLEMS
  9. 5 Derivation of Equations: Integral Equation Approach
    1. 5.1 INTRODUCTION
    2. 5.2 CLASSIFICATION OF INTEGRAL EQUATIONS
    3. 5.3 DERIVATION OF INTEGRAL EQUATIONS
    4. 5.4 GENERAL FORMULATION OF THE EIGENVALUE PROBLEM
    5. 5.5 SOLUTION OF INTEGRAL EQUATIONS
    6. 5.6 RECENT CONTRIBUTIONS
    7. REFERENCES
    8. PROBLEMS
  10. 6 Solution Procedure: Eigenvalue and Modal Analysis Approach
    1. 6.1 INTRODUCTION
    2. 6.2 GENERAL PROBLEM
    3. 6.3 SOLUTION OF HOMOGENEOUS EQUATIONS: SEPARATION‐OF‐VARIABLES TECHNIQUE
    4. 6.4 STURM–LIOUVILLE PROBLEM
    5. 6.5 GENERAL EIGENVALUE PROBLEM
    6. 6.6 SOLUTION OF NONHOMOGENEOUS EQUATIONS
    7. 6.7 FORCED RESPONSE OF VISCOUSLY DAMPED SYSTEMS
    8. 6.8 RECENT CONTRIBUTIONS
    9. REFERENCES
    10. PROBLEMS
  11. 7 Solution Procedure: Integral Transform Methods
    1. 7.1 INTRODUCTION
    2. 7.2 FOURIER TRANSFORMS
    3. 7.3 FREE VIBRATION OF A FINITE STRING
    4. 7.4 FORCED VIBRATION OF A FINITE STRING
    5. 7.5 FREE VIBRATION OF A BEAM
    6. 7.6 LAPLACE TRANSFORMS
    7. 7.7 FREE VIBRATION OF A STRING OF FINITE LENGTH
    8. 7.8 FREE VIBRATION OF A BEAM OF FINITE LENGTH
    9. 7.9 FORCED VIBRATION OF A BEAM OF FINITE LENGTH
    10. 7.10 RECENT CONTRIBUTIONS
    11. REFERENCES
    12. PROBLEMS
  12. 8 Transverse Vibration of Strings
    1. 8.1 INTRODUCTION
    2. 8.2 EQUATION OF MOTION
    3. 8.3 INITIAL AND BOUNDARY CONDITIONS
    4. 8.4 FREE VIBRATION OF AN INFINITE STRING
    5. 8.5 FREE VIBRATION OF A STRING OF FINITE LENGTH
    6. 8.6 FORCED VIBRATION
    7. 8.7 RECENT CONTRIBUTIONS
    8. NOTE
    9. REFERENCES
    10. PROBLEMS
  13. 9 Longitudinal Vibration of Bars
    1. 9.1 INTRODUCTION
    2. 9.2 EQUATION OF MOTION USING SIMPLE THEORY
    3. 9.3 FREE VIBRATION SOLUTION AND NATURAL FREQUENCIES
    4. 9.4 FORCED VIBRATION
    5. 9.5 RESPONSE OF A BAR SUBJECTED TO LONGITUDINAL SUPPORT MOTION
    6. 9.6 RAYLEIGH THEORY
    7. 9.7 BISHOP'S THEORY
    8. 9.8 RECENT CONTRIBUTIONS
    9. REFERENCES
    10. PROBLEMS
  14. 10 Torsional Vibration of Shafts
    1. 10.1 INTRODUCTION
    2. 10.2 ELEMENTARY THEORY: EQUATION OF MOTION
    3. 10.3 FREE VIBRATION OF UNIFORM SHAFTS
    4. 10.4 FREE VIBRATION RESPONSE DUE TO INITIAL CONDITIONS: MODAL ANALYSIS
    5. 10.5 FORCED VIBRATION OF A UNIFORM SHAFT: MODAL ANALYSIS
    6. 10.6 TORSIONAL VIBRATION OF NONCIRCULAR SHAFTS: SAINT‐VENANT'S THEORY
    7. 10.7 TORSIONAL VIBRATION OF NONCIRCULAR SHAFTS, INCLUDING AXIAL INERTIA
    8. 10.8 TORSIONAL VIBRATION OF NONCIRCULAR SHAFTS: THE TIMOSHENKO–GERE THEORY
    9. 10.9 TORSIONAL RIGIDITY OF NONCIRCULAR SHAFTS
    10. 10.10 PRANDTL'S MEMBRANE ANALOGY
    11. 10.11 RECENT CONTRIBUTIONS
    12. REFERENCES
    13. PROBLEMS
  15. 11 Transverse Vibration of Beams
    1. 11.1 INTRODUCTION
    2. 11.2 EQUATION OF MOTION: THE EULER–BERNOULLI THEORY
    3. 11.3 FREE VIBRATION EQUATIONS
    4. 11.4 FREE VIBRATION SOLUTION
    5. 11.5 FREQUENCIES AND MODE SHAPES OF UNIFORM BEAMS
    6. 11.6 ORTHOGONALITY OF NORMAL MODES
    7. 11.7 FREE VIBRATION RESPONSE DUE TO INITIAL CONDITIONS
    8. 11.8 FORCED VIBRATION
    9. 11.9 RESPONSE OF BEAMS UNDER MOVING LOADS
    10. 11.10 TRANSVERSE VIBRATION OF BEAMS SUBJECTED TO AXIAL FORCE
    11. 11.11 VIBRATION OF A ROTATING BEAM
    12. 11.12 NATURAL FREQUENCIES OF CONTINUOUS BEAMS ON MANY SUPPORTS
    13. 11.13 BEAM ON AN ELASTIC FOUNDATION
    14. 11.14 RAYLEIGH'S THEORY
    15. 11.15 TIMOSHENKO'S THEORY
    16. 11.16 COUPLED BENDING–TORSIONAL VIBRATION OF BEAMS
    17. 11.17 TRANSFORM METHODS: FREE VIBRATION OF AN INFINITE BEAM
    18. 11.18 RECENT CONTRIBUTIONS
    19. REFERENCES
    20. PROBLEMS
  16. 12 Vibration of Circular Rings and Curved Beams
    1. 12.1 INTRODUCTION
    2. 12.2 EQUATIONS OF MOTION OF A CIRCULAR RING
    3. 12.3 IN‐PLANE FLEXURAL VIBRATIONS OF RINGS
    4. 12.4 FLEXURAL VIBRATIONS AT RIGHT ANGLES TO THE PLANE OF A RING
    5. 12.5 TORSIONAL VIBRATIONS
    6. 12.6 EXTENSIONAL VIBRATIONS
    7. 12.7 VIBRATION OF A CURVED BEAM WITH VARIABLE CURVATURE
    8. 12.8 RECENT CONTRIBUTIONS
    9. REFERENCES
    10. PROBLEMS
  17. 13 Vibration of Membranes
    1. 13.1 INTRODUCTION
    2. 13.2 EQUATION OF MOTION
    3. 13.3 WAVE SOLUTION
    4. 13.4 FREE VIBRATION OF RECTANGULAR MEMBRANES
    5. 13.5 FORCED VIBRATION OF RECTANGULAR MEMBRANES
    6. 13.6 FREE VIBRATION OF CIRCULAR MEMBRANES
    7. 13.7 FORCED VIBRATION OF CIRCULAR MEMBRANES
    8. 13.8 MEMBRANES WITH IRREGULAR SHAPES
    9. 13.9 PARTIAL CIRCULAR MEMBRANES
    10. 13.10 RECENT CONTRIBUTIONS
    11. NOTES
    12. REFERENCES
    13. PROBLEMS
  18. 14 Transverse Vibration of Plates
    1. 14.1 INTRODUCTION
    2. 14.2 EQUATION OF MOTION: CLASSICAL PLATE THEORY
    3. 14.3 BOUNDARY CONDITIONS
    4. 14.4 FREE VIBRATION OF RECTANGULAR PLATES
    5. 14.5 FORCED VIBRATION OF RECTANGULAR PLATES
    6. 14.6 CIRCULAR PLATES
    7. 14.7 FREE VIBRATION OF CIRCULAR PLATES
    8. 14.8 FORCED VIBRATION OF CIRCULAR PLATES
    9. 14.9 EFFECTS OF ROTARY INERTIA AND SHEAR DEFORMATION
    10. 14.10 PLATE ON AN ELASTIC FOUNDATION
    11. 14.11 TRANSVERSE VIBRATION OF PLATES SUBJECTED TO IN‐PLANE LOADS
    12. 14.12 VIBRATION OF PLATES WITH VARIABLE THICKNESS
    13. 14.13 RECENT CONTRIBUTIONS
    14. REFERENCES
    15. PROBLEMS
  19. 15 Vibration of Shells
    1. 15.1 INTRODUCTION AND SHELL COORDINATES
    2. 15.2 STRAIN–DISPLACEMENT RELATIONS
    3. 15.3 LOVE'S APPROXIMATIONS
    4. 15.4 STRESS–STRAIN RELATIONS
    5. 15.5 FORCE AND MOMENT RESULTANTS
    6. 15.6 STRAIN ENERGY, KINETIC ENERGY, AND WORK DONE BY EXTERNAL FORCES
    7. 15.7 EQUATIONS OF MOTION FROM HAMILTON'S PRINCIPLE
    8. 15.8 CIRCULAR CYLINDRICAL SHELLS
    9. 15.9 EQUATIONS OF MOTION OF CONICAL AND SPHERICAL SHELLS
    10. 15.10 EFFECT OF ROTARY INERTIA AND SHEAR DEFORMATION
    11. 15.11 RECENT CONTRIBUTIONS
    12. NOTES
    13. REFERENCES
    14. PROBLEMS
  20. 16 Vibration of Composite Structures
    1. 16.1 INTRODUCTION
    2. 16.2 CHARACTERIZATION OF A UNIDIRECTIONAL LAMINA WITH LOADING PARALLEL TO THE FIBERS
    3. 16.3 DIFFERENT TYPES OF MATERIAL BEHAVIOR
    4. 16.4 CONSTITUTIVE EQUATIONS OR STRESS–STRAIN RELATIONS
    5. 16.5 COORDINATE TRANSFORMATIONS FOR STRESSES AND STRAINS
    6. 16.6 LAMINA WITH FIBERS ORIENTED AT AN ANGLE
    7. 16.7 COMPOSITE LAMINA IN PLANE STRESS
    8. 16.8 LAMINATED COMPOSITE STRUCTURES
    9. 16.9 VIBRATION ANALYSIS OF LAMINATED COMPOSITE PLATES
    10. 16.10 VIBRATION ANALYSIS OF LAMINATED COMPOSTE BEAMS
    11. 16.11 RECENT CONTRIBUTIONS
    12. REFERENCES
    13. PROBLEMS
  21. 17 Approximate Analytical Methods
    1. 17.1 INTRODUCTION
    2. 17.2 RAYLEIGH'S QUOTIENT
    3. 17.3 RAYLEIGH'S METHOD
    4. 17.4 RAYLEIGH–RITZ METHOD
    5. 17.5 ASSUMED MODES METHOD
    6. 17.6 WEIGHTED RESIDUAL METHODS
    7. 17.7 GALERKIN'S METHOD
    8. 17.8 COLLOCATION METHOD
    9. 17.9 SUBDOMAIN METHOD
    10. 17.10 LEAST SQUARES METHOD
    11. 17.11 RECENT CONTRIBUTIONS
    12. REFERENCES
    13. PROBLEMS
  22. 18 Numerical Methods: Finite Element Method
    1. 18.1 INTRODUCTION
    2. 18.2 FINITE ELEMENT PROCEDURE
    3. 18.3 ELEMENT MATRICES OF DIFFERENT STRUCTURAL PROBLEMS
    4. 18.4 DYNAMIC RESPONSE USING THE FINITE ELEMENT METHOD
    5. 18.5 ADDITIONAL AND RECENT CONTRIBUTIONS
    6. NOTE
    7. REFERENCES
    8. PROBLEMS
  23. A: Basic Equations of Elasticity
    1. A.1 STRESS
    2. A.2 STRAIN–DISPLACEMENT RELATIONS
    3. A.3 ROTATIONS
    4. A.4 STRESS–STRAIN RELATIONS
    5. A.5 EQUATIONS OF MOTION IN TERMS OF STRESSES
    6. A.6 EQUATIONS OF MOTION IN TERMS OF DISPLACEMENTS
  24. B: Laplace and Fourier Transforms
  25. Index
  26. End User License Agreement

Product information

  • Title: Vibration of Continuous Systems, 2nd Edition
  • Author(s): Singiresu S. Rao
  • Release date: March 2019
  • Publisher(s): Wiley
  • ISBN: 9781119424147