928 Pages 173 B/W Illustrations
    by CRC Press

    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.

    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

    Biography

    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.

    "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