Engineering Vibrations: 2nd Edition (Hardback) book cover

Engineering Vibrations

2nd Edition

By William J. Bottega

CRC Press

927 pages | 173 B/W Illus.

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Hardback: 9781439830352
pub: 2014-12-11
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Description

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.

Reviews

"This book is a pleasure to read. The book is very thorough and rigorous, yet it is student-friendly with very readable text and excellent illustrative examples."

—Haim Baruh, Rutgers University, New Brunswick, New Jersey, USA

"The book’s breadth of coverage, and the depth of its treatment of the mathematical foundations of the subject, makes it valuable as either a reference or a text for either a practitioner or a first graduate-level course in vibrations. …As sound and complete a foundation for vibration of two-dimensional continua as you will find anywhere. If you have only one reference on the subject, this is the one to have."

—J. A. M. Boulet, The University of Tennessee, Knoxville, USA

"In the field of vibration analysis, it is useful to observe many points of view and also gain insight as various experts approach a problem and then go about solving it. I would certainly recommend Bottega's Engineering Vibrations as a companion to some of the classical references."

—Noise Control Engineering, March-April 2017

Table of Contents

PRELIMINARIES

Degrees of Freedom

Equivalent Systems

Springs Connected in Parallel and in Series

A Brief Review of Complex Numbers

A Review of Elementary Dynamics

Concluding Remarks

Bibliography

Problems

FREE VIBRATION OF SINGLE DEGREE OF FREEDOM SYSTEMS

Free Vibration of Undamped Systems

Free Vibration of Systems with Viscous Damping

Coulomb (Dry Friction) Damping

Concluding Remarks

Bibliography

Problems

FORCED VIBRATION OF SINGLE DEGREE OF FREEDOM SYSTEMS – 1: PERIODIC EXCITATION

Standard Form of the Equation of Motion

Superposition

Harmonic Forcing

Structural Damping

Selected Applications

Response to General Periodic Loading

Concluding Remarks

Bibliography

Problems

FORCED VIBRATION OF SINGLE DEGREE OF FREEDOM SYSTEMS – 2: NONPERIODIC EXCITATION

Two Generalized Functions

Impulse Response

Response to Arbitrary Excitation

Response to Step Loading

Response to Ramp Loading

Transient Response by Superposition

Shock Spectra

Concluding Remarks

Bibliography

Problems

OPERATIONAL METHODS

The Laplace Transform

Free Vibrations

Forced Vibrations

Concluding Remarks

Bibliography

Problems

DYNAMICS OF MULTI-DEGREE OF FREEDOM SYSTEMS

Newtonian Mechanics of Discrete Systems

Lagrange’s Equations

Symmetry of the System Matrices

Concluding Remarks

Bibliography

Problems

FREE VIBRATION OF MULTI-DEGREE OF FREEDOM SYSTEMS

The General Free Vibration Problem and Its Solution

Unrestrained Systems

Properties of Modal Vectors

Systems with Viscous Damping

Evaluation of Amplitudes and Phase Angles

Concluding Remarks

Bibliography

Problems

FORCED VIBRATION OF MULTI-DEGREE OF FREEDOM SYSTEMS

Introduction

Modal Coordinates

General Motion in Terms of the Natural Modes

Decomposition of the Forced Vibration Problem

Solution of Forced Vibration Problems

Mode Isolation

Rayleigh Damping

Systems with General Viscous Damping

Concluding Remarks

Bibliography

Problems

DYNAMICS OF ONE-DIMENSIONAL CONTINUA

Mathematical Description of 1-D Continua

Characterization of Local Deformation

Longitudinal Motion of Elastic Rods

Torsional Motion of Elastic Rods

Transverse Motion of Strings and Cables

Transverse Motion of Elastic Beams

Geometrically Nonlinear Beam Theory

Translating 1-D Continua

Concluding Remarks

Bibliography

Problems

FREE VIBRATION OF ONE-DIMENSIONAL CONTINUA

The General Free Vibration Problem

Free Vibration of Uniform Second Order Systems

Free Vibration of Euler-Bernoulli Beams

Free Vibration of Euler-Bernoulli Beam-Columns

Free Vibration of Rayleigh Beams

Free Vibration of Timoshenko Beams

Normalization of the Modal Functions

Orthogonality of the Modal Functions

Evaluation of Amplitudes and Phase Angles

Concluding Remarks

Bibliography

Problems

FORCED VIBRATION OF ONE-DIMENSIONAL CONTINUA

Modal Expansion

Decomposition of the Forced Vibration Problem

Solution of Forced Vibration Problems

Steady State Response of One-Dimensional Continua with Structural Damping

Concluding Remarks

Bibliography

Problems

DYNAMICS OF TWO-DIMENSIONAL CONTINUA

Characterization of Local Deformation

Membranes

Elastic Plates

Concluding Remarks

Bibliography

Problems

FREE VIBRATION OF TWO-DIMENSIONAL CONTINUA

The Scalar Product and Orthogonality

The General Free Vibration Problem

Free Vibration of Ideal Membranes

Free Vibration of Kirchhoff Plates

Free Vibration of Uniformly Stretched von Karman Plates

Free Vibration of Mindlin Plates

Normalization of the Modal Functions

Orthogonality of the Modal Functions

Evaluation of Amplitudes and Phase Angles

Concluding Remarks

Bibliography

Problems

FORCED VIBRATION OF TWO-DIMENSIONAL CONTINUA

Mathematical Representation of Point Loads for Two-Dimensional Continua

Forced Vibration of Systems with One Dependent Variable

Forced Vibration of Systems with Multiple Dependent Variables: Mindlin Plates

Steady State Response of Two-Dimensional Continua with Structural Damping

Concluding Remarks

Bibliography

Problems

INDEX

About the Author

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.

Subject Categories

BISAC Subject Codes/Headings:
TEC009020
TECHNOLOGY & ENGINEERING / Civil / General
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical