Engineering Vibrations

ISBN-10: 0849334209
ISBN-13: 9780849334207
Edition: 2006
List price: $159.95
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Description: Integrating the physical and mathematical aspects of vibration, this text emphasizes fundamental principles along with practical problem solving with a mathematically rigorous yet accessible approach. The author uses illustrative examples and case  More...

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Book details

List price: $159.95
Copyright year: 2006
Publisher: CRC Press LLC
Publication date: 2/17/2006
Binding: Hardcover
Pages: 752
Size: 6.50" wide x 9.25" long x 1.50" tall
Weight: 2.596
Language: English

Integrating the physical and mathematical aspects of vibration, this text emphasizes fundamental principles along with practical problem solving with a mathematically rigorous yet accessible approach. The author uses illustrative examples and case studies to reinforce the concepts, encourage effective interpretation of results, and assist in learning the techniques and procedures. The book includes more than 500 illustrations, including two- and three-dimensional drawings, along with tabulated results of case studies and a table of operators of various one-dimensional continua. It also offers problem-solving flowcharts for solving forced vibration problems for discrete and continuous systems.

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 &3- 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

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