Table of Contents
INTRODUCTION TO VIBRATION AND THE FREE RESPONSE
1.1 Introduction to Free Vibration
1.2 Harmonic Motion
1.3 Viscous Damping
1.4 Modeling and Energy Methods
1.5 Stiffness
1.6 Measurement
1.7 Desig
...
Table of Contents
INTRODUCTION TO VIBRATION AND THE FREE RESPONSE
1.1 Introduction to Free Vibration
1.2 Harmonic Motion
1.3 Viscous Damping
1.4 Modeling and Energy Methods
1.5 Stiffness
1.6 Measurement
1.7 Design Considerations
1.8 Stability
1.9 Numerical Integration of the Time Response
1.10 Coulomb Friction and the Pendulum
Problems
RESPONSE TO HARMONIC EXCITATION
2.1 Harmonic Excitation of Undamped Systems
2.2 Harmonic Excitation of Damped Systems
2.3 Alternative Representations
2.4 Base Excitation
2.5 Rotating Unbalance
2.6 Measurement Devices
2.7 Other Forms of Damping
2.8 Numerical Integration and Design
2.9 Nonlinear Response Properties
Problems
GENERAL FORCED RESPONSE
3.1 Impulse Response Function
3.2 Response to an Arbitrary Input
3.3 Response to an Arbitrary Periodic Input
3.4 Transform Methods
3.5 Response to Random Inputs
3.6 Shock Spectrum
3.7 Measurement via Transfer Functions
3.8 Stability
3.9 Numerical Integration of the Response
3.10 Nonlinear Response Properties
Problems
MULTIPLE-DEGREE-OF-FREEDOM SYSTEMS
4.1 Two-Degree-of-Freedom Model (Undamped)
4.2 Eigenvalues and Natural Frequencies
4.3 Modal Analysis
4.4 More Than Two Degrees of Freedom
4.5 Systems with Viscous Damping
4.6 Modal Analysis of the Forced Response
4.7 Lagrange’s Equations
4.8 Examples
4.9 Computational Eigenvalue Problems for Vibration
4.10 Numerical Integration of the Time Response
Problems
DESIGN FOR VIBRATION SUPPRESSION
5.1 Acceptable Levels of Vibration
5.2 Vibration Isolation
5.3 Vibration Absorbers
5.4 Damping in Vibration Absorption
5.5 Optimization
5.6 Viscoelastic Damping Treatments
5.7 Critical Speeds of Rotating Disks
5.8 Approximation and Scaling
Problems
DISTRIBUTED-PARAMETER SYSTEMS
6.1 Vibration of a String or Cable
6.2 Modes and Natural Frequencies
6.3 Vibration of Rods and Bars
6.4 Torsional Vibration
6.5 Bending Vibration of a Beam
6.6 Vibration of Membranes and Plates
6.7 Models of Damping
6.8 Modal Analysis of the Forced Response
Problems
VIBRATION TESTING AND EXPERIMENTAL MODAL ANALYSIS
7.1 Measurement Hardware
7.2 Digital Signal Processing
7.3 Random Signal Analysis in Testing
7.4 Modal Data Extraction
7.5 Modal Parameters by Circle Fitting
7.6 Mode Shape Measurement
7.7 Vibration Testing for Endurance and Diagnostics
7.8 Operational Deflection Shape Measurement
Problems
FINITE ELEMENT METHOD
8.1 Example: The Bar
8.2 Three-Element Bar
8.3 Beam Elements
8.4 Lumped-Mass Matrices
8.5 Trusses
8.6 Model Reduction
Problems
Appendices
COMPLEX NUMBERS AND FUNCTIONS
LAPLACE TRANSFORMS
MATRIX BASICS
THE VIBRATION LITERATURE
LIST OF SYMBOLS
CODES AND WEB SITES
UNITS AND CONVERSIONS
REFERENCES
ANSWERS TO SELECTED PROBLEMS
INDEXTable of Contents
INTRODUCTION TO VIBRATION AND THE FREE RESPONSE
1.1 Introduction to Free Vibration
1.2 Harmonic Motion
1.3 Viscous Damping
1.4 Modeling and Energy Methods
1.5 Stiffness
1.6 Measurement
1.7 Design Considerations
1.8 Stability
1.9 Numerical Integration of the Time Response
1.10 Coulomb Friction and the Pendulum
Problems
RESPONSE TO HARMONIC EXCITATION
2.1 Harmonic Excitation of Undamped Systems
2.2 Harmonic Excitation of Damped Systems
2.3 Alternative Representations
2.4 Base Excitation
2.5 Rotating Unbalance
2.6 Measurement Devices
2.7 Other Forms of Damping
2.8 Numerical Integration and Design
2.9 Nonlinear Response Properties
Problems
GENERAL FORCED RESPONSE
3.1 Impulse Response Function
3.2 Response to an Arbitrary Input
3.3 Response to an Arbitrary Periodic Input
3.4 Transform Methods
3.5 Response to Random Inputs
3.6 Shock Spectrum
3.7 Measurement via Transfer Functions
3.8 Stability
3.9 Numerical Integration of the Response
3.10 Nonlinear Response Properties
Problems
MULTIPLE-DEGREE-OF-FREEDOM SYSTEMS
4.1 Two-Degree-of-Freedom Model (Undamped)
4.2 Eigenvalues and Natural Frequencies
4.3 Modal Analysis
4.4 More Than Two Degrees of Freedom
4.5 Systems with Viscous Damping
4.6 Modal Analysis of the Forced Response
4.7 Lagrange’s Equations
4.8 Examples
4.9 Computational Eigenvalue Problems for Vibration
4.10 Numerical Integration of the Time Response
Problems
DESIGN FOR VIBRATION SUPPRESSION
5.1 Acceptable Levels of Vibration
5.2 Vibration Isolation
5.3 Vibration Absorbers
5.4 Damping in Vibration Absorption
5.5 Optimization
5.6 Viscoelastic Damping Treatments
5.7 Critical Speeds of Rotating Disks
5.8 Approximation and Scaling
Problems
DISTRIBUTED-PARAMETER SYSTEMS
6.1 Vibration of a String or Cable
6.2 Modes and Natural Frequencies
6.3 Vibration of Rods and Bars
6.4 Torsional Vibration
6.5 Bending Vibration of a Beam
6.6 Vibration of Membranes and Plates
6.7 Models of Damping
6.8 Modal Analysis of the Forced Response
Problems
VIBRATION TESTING AND EXPERIMENTAL MODAL ANALYSIS
7.1 Measurement Hardware
7.2 Digital Signal Processing
7.3 Random Signal Analysis in Testing
7.4 Modal Data Extraction
7.5 Modal Parameters by Circle Fitting
7.6 Mode Shape Measurement
7.7 Vibration Testing for Endurance and Diagnostics
7.8 Operational Deflection Shape Measurement
Problems
FINITE ELEMENT METHOD
8.1 Example: The Bar
8.2 Three-Element Bar
8.3 Beam Elements
8.4 Lumped-Mass Matrices
8.5 Trusses
8.6 Model Reduction
Problems
Appendices
COMPLEX NUMBERS AND FUNCTIONS
LAPLACE TRANSFORMS
MATRIX BASICS
THE VIBRATION LITERATURE
LIST OF SYMBOLS
CODES AND WEB SITES
UNITS AND CONVERSIONS
REFERENCES
ANSWERS TO SELECTED PROBLEMS
INDEX
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