**Engineering Vibrations 2nd Edition by William J. Bottega, ISBN-13: 978-1439830352**

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- Publisher: CRC Press; 2nd edition (December 11, 2014)
- Language: English
- 928 pages
- ISBN-10: 1439830355
- ISBN-13: 978-1439830352

A thorough study of the oscillatory and transient motion of mechanical and structural systems, * Engineering Vibrations, Second Edition* presents vibrations from a unified point of view, and builds on the first edition with additional chapters and sections that contain more advanced, graduate-level topics. Using numerous examples and case studies to reinforce concepts, the author reviews basic principles, incorporates advanced abstract concepts from first principles, and weaves together physical interpretation and fundamental principles with applied problem solving. For each class of system, the text explores the fundamental dynamics and studies free and forced vibrations. This revised version combines the physical and mathematical facets of vibration, and emphasizes the connecting ideas, concepts, and techniques.

What’s New in the Second Edition:

- Includes a section on the forced response of structurally damped one-dimensional continua
- Adds three new chapters: Dynamics of Two-Dimensional Continua, Free Vibration of Two-Dimensional Continua, and Forced Vibration of Two-Dimensional Continua
- Addresses the linear and geometrically nonlinear characterization of three-dimensional deformation for mathematically two-dimensional structures, and the dynamics and vibration of various types of structures within this class
- Covers deformation, dynamics, and vibration of membranes, of Kirchhoff plates, of von Karman plates, and of Mindlin plates
- Details a full development for the characterization of deformation and motion for mathematically two-dimensional continua
- Discusses the free and forced vibration of two-dimensional continua and the steady state response of two-dimensional continua with structural damping

* Engineering Vibrations, Second Edition *offers a systematic and unified treatment of mechanical and structural vibrations, and provides you with a complete overview of vibration theory and analysis.

**Table of Contents:**

Cover

Half-Title Page

Title Page

Copyright Page

Dedication

Table of Contents

Preface To The Second Edition

Preface To The First Edition

About The Author

1. Preliminaries

1.1 Degrees of Freedom

1.2 Equivalent Systems

1.2.1 Extension/Contraction of Elastic Rods

1.2.2 Bending of Elastic Beams

1.2.3 Torsion of Elastic Rods

1.2.4 Floating Bodies

1.2.5 The Viscous Damper

1.2.6 Aero/Hydrodynamic Damping (Drag)

1.3 Springs Connected in Parallel and in Series

1.3.1 Springs in Parallel

1.3.2 Springs in Series

1.4 A Brief Review of Complex Numbers

1.5 A Review of Elementary Dynamics

1.5.1 Kinematics of Particles

1.5.2 Kinetics of a Single Particle

1.5.3 Dynamics of Particle Systems

1.5.4 Kinematics of Rigid Bodies

1.5.5 (Planar) Kinetics of Rigid Bodies

1.6 Concluding Remarks

Bibliography

Problems

2. Free Vibration Of Single Degree Of Freedom Systems

2.1 Free Vibration of Undamped Systems

2.1.1 Governing Equation and System Response

2.1.2 The Effect of Gravity

2.1.3 Work and Energy

2.1.4 The Simple Pendulum

2.2 Free Vibration of Systems with Viscous Damping

2.2.1 Equation of Motion and General System Response

2.2.2 Underdamped Systems

2.2.3 Logarithmic Decrement

2.2.4 Overdamped Systems

2.2.5 Critically Damped Systems

2.3 Coulomb (Dry Friction) Damping

2.3.1 Stick-Slip Condition

2.3.2 System Response

2.4 Concluding Remarks

Bibliography

Problems

3. Forced Vibration Of Single Degree Of Freedom Systems – 1: Periodic Excitation

3.1 Standard Form of the Equation of Motion

3.2 Superposition

3.3 Harmonic Forcing

3.3.1 Formulation

3.3.2 Steady State Response of Undamped Systems

3.3.3 Steady State Response of Systems with Viscous Damping

3.3.4 Force Transmission and Vibration Isolation

3.4 Structural Damping

3.4.1 Linear Hereditary Materials

3.4.2 Steady State Response of Linear Hereditary Materials

3.4.3 Steady State Response of Single Degree of Freedom Systems

3.5 Selected Applications

3.5.1 Harmonic Motion of the Support

3.5.2 Unbalanced Motor

3.5.3 Synchronous Whirling of Rotating Shafts

3.6 Response to General Periodic Loading

3.6.1 General Periodic Excitation

3.6.2 Steady State Response

3.7 Concluding Remarks

Bibliography

Problems

4. Forced Vibration Of Single Degree Of Freedom Systems – 2: Nonperiodic Excitation

4.1 Two Generalized Functions

4.1.1 The Dirac Delta Function (Unit Impulse)

4.1.2 The Heaviside Step Function (Unit Step)

4.1.3 Relation Between the Unit Step and the Unit Impulse

4.2 Impulse Response

4.2.1 Impulsive and Nonimpulsive Forces

4.2.2 Response to an Applied Impulse

4.3 Response to Arbitrary Excitation

4.4 Response to Step Loading

4.5 Response to Ramp Loading

4.6 Transient Response by Superposition

4.6.1 The Rectangular Pulse

4.6.2 Linear Transition to Constant Load Level

4.7 Shock Spectra

4.8 Concluding Remarks

Bibliography

Problems

5. Operational Methods

5.1 The Laplace Transform

5.1.1 Laplace Transforms of Basic Functions

5.1.2 Shifting Theorem

5.1.3 Laplace Transforms of the Derivatives of Functions

5.1.4 Convolution

5.2 Free Vibrations

5.3 Forced Vibrations

5.3.1 The Governing Equations

5.3.2 Steady State Response

5.3.3 Transient Response

5.4 Concluding Remarks

Bibliography

Problems

6. Dynamics Of Multi-Degree Of Freedom Systems

6.1 Newtonian Mechanics of Discrete Systems

6.1.1 Mass-Spring Systems

6.1.2 The Double Pendulum

6.1.3 Two-Dimensional Motion of a Rigid Frame

6.2 Lagrange’s Equations

6.2.1 Virtual Work

6.2.2 The Canonical Equations

6.2.3 Implementation

6.2.4 The Rayleigh Dissipation Function

6.3 Symmetry of the System Matrices

6.3.1 The Stiffness Matrix

6.3.2 The Mass Matrix

6.3.3 The Damping Matrix

6.4 Concluding Remarks

Bibliography

Problems

7. Free Vibration Of Multi-Degree Of Freedom Systems

7.1 The General Free Vibration Problem and Its Solution

7.2 Unrestrained Systems

7.3 Properties of Modal Vectors

7.3.1 The Scalar Product

7.3.2 Orthogonality of the Modes

7.3.3 Normalization

7.4 Systems with Viscous Damping

7.4.1 System Response

7.4.2 State Space Representation

7.5 Evaluation of Amplitudes and Phase Angles

7.5.1 Undamped Systems

7.5.2 Systems with General Viscous Damping

7.6 Concluding Remarks

Bibliography

Problems

8. Forced Vibration Of Multi-Degree Of Freedom Systems

8.1 Introduction

8.1.1 Steady State Response to Harmonic Excitation

8.1.2 The Simple Vibration Absorber

8.2 Modal Coordinates

8.2.1 Principal Coordinates

8.2.2 Coordinate Transformations

8.2.3 Modal Coordinates

8.3 General Motion in Terms of the Natural Modes

8.3.1 Linear Independence of the Set of Modal Vectors

8.3.2 Modal Expansion

8.4 Decomposition of the Forced Vibration Problem

8.5 Solution of Forced Vibration Problems

8.6 Mode Isolation

8.7 Rayleigh Damping

8.8 Systems with General Viscous Damping

8.8.1 Steady State Response to Harmonic Excitation

8.8.2 Eigenvector Expansion

8.8.3 Decomposition of the Forced Vibration Problem

8.8.4 Solution of Forced Vibration Problems

8.9 Concluding Remarks

Bibliography

Problems

9. Dynamics Of One-Dimensional Continua

9.1 Mathematical Description of 1-D Continua

9.1.1 Correspondence Between Discrete and Continuous Systems

9.1.2 The Scalar Product and Orthogonality

9.2 Characterization of Local Deformation

9.2.1 Relative Extension of a Material Line Element

9.2.2 Distortion

9.3 Longitudinal Motion of Elastic Rods

9.4 Torsional Motion of Elastic Rods

9.5 Transverse Motion of Strings and Cables

9.6 Transverse Motion of Elastic Beams

9.6.1 Kinematical and Constitutive Relations

9.6.2 Kinetics

9.6.3 Euler-Bernoulli Beam Theory

9.6.4 Rayleigh Beam Theory

9.6.5 Timoshenko Beam Theory

9.7 Geometrically Nonlinear Beam Theory

9.8 Translating 1-D Continua

9.8.1 Kinematics of a Material Particle

9.8.2 Kinetics

9.9 Concluding Remarks

Bibliography

Problems

10. Free Vibration Of One-Dimensional Continua

10.1 The General Free Vibration Problem

10.2 Free Vibration of Uniform Second Order Systems

10.2.1 The General Free Vibration Problem and Its Solution

10.2.2 Longitudinal Vibration of Elastic Rods

10.2.3 Torsional Vibration of Elastic Rods

10.2.4 Transverse Vibration of Strings and Cables

10.3 Free Vibration of Euler-Bernoulli Beams

10.4 Free Vibration of Euler-Bernoulli Beam-Columns

10.5 Free Vibration of Rayleigh Beams

10.6 Free Vibration of Timoshenko Beams

10.7 Normalization of the Modal Functions

10.8 Orthogonality of the Modal Functions

10.8.1 Systems Whose Mass Operators Are Scalar Functions

10.8.2 Second Order Systems

10.8.3 Euler-Bernoulli Beams and Beam-Columns

10.8.4 Rayleigh Beams

10.8.5 Timoshenko Beams

10.9 Evaluation of Amplitudes and Phase Angles

10.9.1 Systems Possessing a Single Scalar Mass Operator

10.9.2 Rayleigh Beams

10.9.3 Timoshenko Beams

10.10 Concluding Remarks

Bibliography

Problems

11. Forced Vibration Of One-Dimensional Continua

11.1 Modal Expansion

11.1.1 Linear Independence of the Modal Functions

11.1.2 Generalized Fourier Series

11.2 Decomposition of the Forced Vibration Problem

11.3 Solution of Forced Vibration Problems

11.3.1 Axially Loaded Elastic Rods

11.3.2 Torsion of Elastic Rods

11.3.3 Strings and Cables

11.3.4 Euler-Bernoulli Beams

11.3.5 Rayleigh Beams

11.3.6 Timoshenko Beams

11.4 Steady State Response of One-Dimensional Continua with Structural Damping

11.4.1 Stiffness Operators for 1-D Continua with Structural Damping

11.4.2 Steady State Response of 1-D Continua with Structural Damping

11.5 Concluding Remarks

Bibliography

Problems

12. Dynamics Of Two-Dimensional Continua

12.1 Characterization of Local Deformation

12.1.1 In-Plane Deformation

12.1.2 Deformation with Out-of-Plane Rotation

12.1.3 Polar Coordinates

12.1.4 Summary of Strain Measures

12.2 Membranes

12.2.1 The Infinitely Flexible Structure

12.2.2 The Ideal Membrane

12.3 Elastic Plates

12.3.1 Kinematical and Constitutive Relations

12.3.2 Kinetics

12.3.3 Kirchhoff Plate Theory

12.3.4 Mindlin Plate Theory

12.3.5 Geometrically Nonlinear (von Karman) Plate Theory

12.4 Concluding Remarks

Bibliography

Problems

13. Free Vibration Of Two-Dimensional Continua

13.1 The Scalar Product and Orthogonality

13.1.1 Systems with One Dependent Variable

13.1.2 Systems with Multiple Dependent Variables

13.2 The General Free Vibration Problem

13.2.1 Systems with One Dependent Variable

13.2.2 Systems with Multiple Dependent Variables

13.3 Free Vibration of Ideal Membranes

13.3.1 Rectangular Membranes

13.3.2 Circular Membranes

13.4 Free Vibration of Kirchhoff Plates

13.4.1 Rectangular Plates

13.4.2 Circular Plates

13.5 Free Vibration of Uniformly Stretched von Karman Plates

13.6 Free Vibration of Mindlin Plates

13.6.1 The General Solution

13.6.2 The Frequency Spectrum

13.6.3 Implementation

13.7 Normalization of the Modal Functions

13.7.1 Systems with One Dependent Variable

13.7.2 Systems with Multiple Dependent Variables

13.8 Orthogonality of the Modal Functions

13.8.1 Systems with One Dependent Variable

13.8.2 Mindlin Plates

13.9 Evaluation of Amplitudes and Phase Angles

13.9.1 Systems Possessing a Single Scalar Mass Operator

13.9.2 Mindlin Plates

13.10 Concluding Remarks

Bibliography

Problems

14. Forced Vibration Of Two-Dimensional Continua

14.1 Mathematical Representation of Point Loads for Two-Dimensional Continua

14.2 Forced Vibration of Systems with One Dependent Variable

14.3 Forced Vibration of Systems with Multiple Dependent Variables: Mindlin Plates

14.4 Steady State Response of Two-Dimensional Continua with Structural Damping

14.4.1 Stiffness Operators for 2-D Continua with Structural Damping

14.4.2 Steady State Response of Kirchhoff and von Karman Plates with Structural Damping

14.4.3 Steady State Response of Mindlin Plates with Structural Damping

14.5 Concluding Remarks

Bibliography

Problems

Index

* William J. Bottega *is Professor of Mechanical and Aerospace Engineering at Rutgers University, where he has been since 1984. He received his Ph.D. in applied mechanics from Yale University, his M.S. in theoretical and applied mechanics from Cornell University, and his B.E. from the City College of New York. He also spent several years in R&D at General Dynamics where he worked on vibration and sound-structure interaction problems. In addition, Dr. Bottega is the author of numerous archival publications on various areas of theoretical and applied mechanics.

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