Cover
Title Page
Copyright
About the Author
Preface to the SI Edition
Preface
Contents
Ch 1: Introduction
1.1 The Study of Vibrations
1.2 Mathematical Modeling
1.3 Generalized Coordinates
1.4 Classification of Vibration
1.5 Dimensional Analysis
1.6 Simple Harmonic Motion
1.7 Review of Dynamics
1.8 Two Benchmark Examples
1.9 Further Examples
1.10 Summary
Problems
Ch 2: Modeling of SDOF Systems
2.1 Introduction
2.2 Springs
2.3 Springs in Combination
2.4 Other Sources of Potential Energy
2.5 Viscous Damping
2.6 Energy Dissipated by Viscous Damping
2.7 Inertia Elements
2.8 External Sources
2.9 Free-Body Diagram Method
2.10 Static Deflections and Gravity
2.11 Small Angle or Displacement Assumption
2.12 Equivalent Systems Method
2.13 Benchmark Examples
2.14 Further Examples
2.15 Chapter Summary
Problems
Ch 3: Free Vibrations of SDOF Systems
3.1 Introduction
3.2 Standard Form of Differential Equation
3.3 Free Vibrations of an Undamped System
3.4 Underdamped Free Vibrations
3.5 Critically Damped Free Vibrations
3.6 Overdamped Free Vibrations
3.7 Coulomb Damping
3.8 Hysteretic Damping
3.9 Other Forms of Damping
3.10 Benchmark Examples
3.11 Further Examples
3.12 Chapter Summary
Problems
Ch 4: Harmonic Excitation of SDOF Systems
4.1 Introduction
4.2 Forced Response of an Undamped System Due to a Single-Frequency Excitation
4.3 Forced Response of a Viscously Damped System Subject to a Single-Frequency Harmonic Excitation
4.4 Frequency-Squared Excitations
4.5 Response due to Harmonic Excitation of Support
4.6 Vibration Isolation
4.7 Vibration Isolation from Frequency-Squared Excitations
4.8 Practical Aspects of Vibration Isolation
4.9 Multifrequency Excitations
4.10 General Periodic Excitations
4.11 Seismic Vibration Measuring Instruments
4.12 Complex Representations
4.13 Systems with Coulomb Damping
4.14 Systems with Hysteretic Damping
4.15 Energy Harvesting
4.16 Benchmark Examples
4.17 Further Examples
4.18 Chapter Summary
Problems
Ch 5: Transient Vibrations of SDOF Systems
5.1 Introduction
5.2 Derivation of Convolution Integral
5.3 Response due to a General Excitation
5.4 Excitations Whose Forms Change at Discrete Times
5.5 Transient Motion due to Base Excitation
5.6 Laplace Transform Solutions
5.7 Transfer Functions
5.8 Numerical Methods
5.9 Shock Spectrum
5.10 Vibration Isolation for Short Duration Pulses
5.11 Benchmark Examples
5.12 Further Examples
5.13 Chapter Summary
Problems
Ch 6: Two Degree-Of-Freedom Systems
6.1 Introduction
6.2 Derivation of the Equations of Motion
6.3 Natural Frequencies and Mode Shapes
6.4 Free Response of Undamped Systems
6.5 Free Vibrations of a System with Viscous Damping
6.6 Principal Coordinates
6.7 Harmonic Response of Two Degree-Of-Freedom Systems
6.8 Transfer Functions
6.9 Sinusoidal Transfer Function
6.10 Frequency Response
6.11 Dynamic Vibration Absorbers
6.12 Damped Vibration Absorbers
6.13 Vibration Dampers
6.14 Benchmark Examples
6.15 Further Examples
6.16 Chapter Summary
Problems
Ch 7: Modeling of MDOF Systems
7.1 Introduction
7.2 Derivation of Differential Equations Using the Free-Body Diagram Method
7.3 Lagrange's Equations
7.4 Matrix Formulation of Differential Equations for Linear Systems
7.5 Stiffness Influence Coefficients
7.6 Flexibility Influence Coefficients
7.7 Inertia Influence Coefficients
7.8 Lumped-Mass Modeling of Continuous Systems
7.9 Benchmark Examples
7.10 Further Examples
7.11 Summary
Problems
Ch 8: Free Vibrations of MDOF Systems
8.1 Introduction
8.2 Normal-Mode Solution
8.3 Natural Frequencies and Mode Shapes
8.4 General Solution
8.5 Special Cases
8.6 Energy Scalar Products
8.7 Properties of Natural Frequencies and Mode Shapes
8.8 Normalized Mode Shapes
8.9 Rayleigh's Quotient
8.10 Principal Coordinates
8.11 Determination of Natural Frequencies and Mode Shapes
8.12 Proportional Damping
8.13 General Viscous Damping
8.14 Benchmark Examples
8.15 Further Examples
8.16 Summary
Problems
Ch 9: Forced Vibrations of MDOF Systems
9.1 Introduction
9.2 Harmonic Excitations
9.3 Laplace Transform Solutions
9.4 Modal Analysis for Undamped Systems and Systems with Proportional Damping
9.5 Modal Analysis for Systems with General Damping
9.6 Numerical Solutions
9.7 Benchmark Examples
9.8 Further Examples
9.9 Chapter Summary
Problems
Ch 10: Vibrations of Continuous Systems
10.1 Introduction
10.2 General Method
10.3 Second-Order Systems: Torsional Oscillations of a Circular Shaft
10.4 Transverse Beam Vibrations
10.5 Energy Methods
10.6 Benchmark Examples
10.7 Chapter Summary
Problems
Ch 11: Finite-Element Method
11.1 Introduction
11.2 Assumed Modes Method
11.3 General Method
11.4 The Bar Element
11.5 Beam Element
11.6 Global Matrices
11.7 Benchmark Example
11.8 Further Examples
11.9 Summary
Problems
Ch 12: Nonlinear Vibrations
12.1 Introduction
12.2 Sources of Nonlinearity
12.3 Qualitative Analysis of Nonlinear Systems
12.4 Quantitative Methods of Analysis
12.5 Free Vibrations of SDOF Systems
12.6 Forced Vibrations of SDOF Systems with Cubic Nonlinearities
12.7 MDOF Systems
12.8 Continuous Systems
12.9 Chaos
12.10 Chapter Summary
Problems
Ch 13: Random Vibrations
13.1 Introduction
13.2 Behavior of a Random Variable
13.3 Functions of a Random Variable
13.4 Joint Probability Distributions
13.5 Fourier Transforms
13.6 Power Spectral Density
13.7 Mean Square Value of the Response
13.8 Benchmark Example
13.9 Summary
Problems
Appendix A Unit Impulse Function and Unit Step Function
Appendix B Laplace Transforms
Appendix C Linear Algebra
Appendix D Deflection of Beams Subject to Concentrated Loads
Appendix E Integrals Used in Random Vibrations
Appendix F Vibes
References
Index