Engineering Vibrations
Purchasing Options
Features
- Provides a systematic and unified presentation of the subject of mechanical and structural vibrations
- Emphasizes physical interpretation, fundamental principles, and problem solving along with rigorous mathematical development
- Offers comprehensive coverage that includes continuous systems and general damping for discrete systems
- Presents in-depth discussions of structural damping along with unique presentations and comparison of dynamics and vibrations of Rayleigh and Timoshenko beams
- Includes extensive illustrations, examples, and case studies
Solutions Manual available with qualifying course adoptions!
Summary
A resource on vibration that imparts a deep physical as well as mathematical understanding is critical to students who first encounter the subject. Books with an overly mathematical focus can leave them without a grasp of the underlying physics and mechanics. Those that attempt to be reader-friendly often oversimplify the mathematics and mechanics, leaving them with a lack of depth and unprepared for advanced work and complex problems. With a carefully balanced approach, Engineering Vibrations provides a systematic and unified treatment of mechanical and structural vibrations along with rigorous yet approachable mathematical development.
This text advances abstract concepts from first principles. The author weaves together the physical interpretation and fundamental principles with applied problem solving and uses illustrative examples and case studies to reinforce the concepts, encourage effective interpretation of results, and assist in learning the techniques and procedures. Accompanied by more than 500 two- and three-dimensional drawings, the book offers tabulated results of case studies and a table of operators of various one-dimensional continua. It also contains problem-solving flowcharts for solving forced vibration problems for discrete and continuous systems. For each class of system, it explores the fundamental dynamics and studies free and forced vibrations under various conditions.
Buildinga solid understanding of the principles and bases for mechanical and structural vibration, Engineering Vibrations offers a comprehensive and accessible introduction to the subject of vibrations and progresses systematically to advanced topics.
Table of Contents
Preliminaries
Degrees of Freedom
Equivalent Systems
. Extension/Contraction of Elastic Rods
. Bending of Elastic Beams
. Torsion of Elastic Rods
. Floating Bodies
. The Viscous Damper
. Aero/Hydrodynamic Damping (Drag)
Springs Connected in Parallel and in Series
. Springs in Parallel
. Springs in Series
A Brief Review of Complex Numbers
A Review of Elementary Dynamics
. Kinematics of Particles
. Kinetics of a Single Particle
. Dynamics of Particle Systems
. Kinematics of Rigid Bodies
. (Planar) Kinetics of Rigid Bodies
Concluding Remarks
Bibliography
Problems
Free Vibration of Single Degree of Freedom Systems
Free Vibration of Undamped Systems
. Governing Equation and System Response
. The Effect of Gravity
. Work and Energy
. The Simple Pendulum
Free Vibration of Systems with Viscous Damping
. Equation of Motion and General System Response
. Underdamped Systems
. Logarithmic Decrement
. Overdamped Systems
. Critically Damped Systems
Coulomb (Dry Friction) Damping
. Stick-Slip Condition
. System Response
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
. Formulation
. Steady State Response of Undamped Systems
. Steady State Response of Systems with Viscous Damping
. Force Transmission and Vibration Isolation
Structural Damping
. Linear Hereditary Materials
. Steady State Response of Linear Hereditary Materials
. Steady State Response of Single Degree of Freedom Systems
Selected Applications
. Harmonic Motion of the Support
. Unbalanced Motor
. Synchronous Whirling of Rotating Shafts
Response to General Periodic Loading
. General Periodic Excitation
. Steady State Response
Concluding Remarks
Bibliography
Problems
Forced Vibration of Single Degree of Freedom Systems – 2: Nonperiodic Excitation
Two Generalized Functions
. The Dirac Delta Function (Unit Impulse)
. The Heaviside Step Function (Unit Step)
. Relation Between the Unit Step and the Unit Impulse
Impulse Response
. Impulsive and Nonimpulsive Forces
. Response to an Applied Impulse
Response to Arbitrary Excitation
Response to Step Loading
Response to Ramp Loading
Transient Response by Superposition
. The Rectangular Pulse
. Linear Transition to Constant Load Level
Shock Spectra
Concluding Remarks
Bibliography
Problems
Operational Methods
The Laplace Transform
. Laplace Transforms of Basic Functions
. Shifting Theorem
. Laplace Transforms of the Derivatives of Functions
. Convolution
Free Vibrations
Forced Vibrations
. The Governing Equations
. Steady State Response
. Transient Response
Concluding Remarks
Bibliography
Problems
Dynamics of Multi-Degree of Freedom Systems
Newtonian Mechanics of Discrete Systems
. Mass-Spring Systems
. The Double Pendulum
. Two-Dimensional Motion of a Rigid Frame
Lagrange’s Equations
. Virtual Work
. The Canonical Equations
. Implementation
. The Rayleigh Dissipation Function
Symmetry of the System Matrices
. The Stiffness Matrix
. The Mass Matrix
. The Damping Matrix
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
. The Scalar Product
. Orthogonality
. Normalization
Systems with Viscous Damping
. System Response
. State Space Representation
Evaluation of Amplitudes and Phase Angles
. Undamped Systems
. Systems with General Viscous Damping
Concluding Remarks
Bibliography
Problems
Forced Vibration of Multi-Degree of Freedom Systems
Introduction
. Steady State Response to Harmonic Excitation
. The Simple Vibration Absorber
Modal Coordinates
. Principal Coordinates
. Coordinate Transformations
. Modal Coordinates
General Motion in Terms of the Natural Modes
. Linear Independence of the Set of Modal Vectors
. Modal Expansion
Decomposition of the Forced Vibration Problem
Solution of Forced Vibration Problems
Mode Isolation
Rayleigh Damping
Systems with General Viscous Damping
. Steady State Response to Harmonic Excitation
. Eigenvector Expansion
. Decomposition of the Forced Vibration Problem
. Solution of Forced Vibration Problems
Concluding Remarks
Bibliography
Problems
Dynamics of One-Dimensional Continua
Mathematical Description of 1-D Continua
. Correspondence Between Discrete and Continuous Systems
. The Scalar Product and Orthogonality
Characterization of Local Deformation
. Relative Extension of a Material Line Element
. Distortion
Longitudinal Motion of Elastic Rods
Torsional Motion of Elastic Rods
Transverse Motion of Strings and Cables
Transverse Motion of Elastic Beams
. Kinematical and Constitutive Relations
. Kinetics
. Euler-Bernoulli Beam Theory
. Rayleigh Beam Theory
. Timoshenko Beam Theory
Geometrically Nonlinear Beam Theory
Translating 1-D Continua
. Kinematics of a Material Particle
. Kinetics
Concluding Remarks
Bibliography
Problems
Free Vibration of One-Dimensional Continua
The General Free Vibration Problem
Free Vibration of Uniform Second Order Systems
. The General Free Vibration Problem and Its Solution
. Longitudinal Vibration of Elastic Rods
. Torsional Vibration of Elastic Rods
. Transverse Vibration of Strings and Cables
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
. Systems Whose Mass Operators Are Scalar Functions
. Second Order Systems
. Euler-Bernoulli Beams and Beam-Columns
. Rayleigh Beams
. Timoshenko Beams
Evaluation of Amplitudes and Phase Angles
. Systems Possessing a Single Scalar Mass Operator
. Rayleigh Beams
. Timoshenko Beams
Concluding Remarks
Bibliography
Problems
Forced Vibration of One-Dimensional Continua
Modal Expansion
. Linear Independence of the Modal Functions
. Generalized Fourier Series
Decomposition of the Forced Vibration Problem
Solution of Forced Vibration Problems
. Axially Loaded Elastic Rods
. Torsion of Elastic Rods
. Strings and Cables
. Euler-Bernoulli Beams
. Rayleigh Beams
. Timoshenko Beams
Concluding Remarks
Bibliography
Problems
Index
Editorial Reviews
“A tremendous amount of experience is distilled in this book on engineering vibrations. I am deeply impressed by the brilliance of selection and organization of topics and chapter, technical format and clear and instructive styles, which all result from a rigorous understanding of the need for a book of this scope. The book certainly should be considered an important contribution to the study of engineering vibrations as understandably and appropriately visualized by the author…There is little doubt that each chapter is well and expertly written and well presented. Anyone with serious interest in the study of mechanical and structural vibrations will find this book almost a ‘must have’.”
—Current Engineering Practice, Volume 48, Issue 6
“… balances physics/mechanics and mathematics in this wide-ranging resource for students and professionals working on mechanical and structural vibration. With illustrations, examples and case studies supplementing the text … Each topic includes a bibliography and exercises.”
—Scitech Book News, December 2006
"...a thoroughly self-consistent and comprehensive book that is both easy to read and mathematically rigorous."
—International Jouranl of Acoustics and Vibration, March 2008
"This book provides a systematic and unified presentation of mechanical and structural vibrations, emphasizing the physical interpretation, fundamental principles and problem solving. This advantage is coupled with rigorous mathematical developments in a form which is readable to advanced undergraduate and graduate university students in engineering and related fields."
—Eugeni Syrkin, in Zentralblatt MATH, 2008
