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## Book Description

In this textbook all the basic concepts in mechanical vibrations are clearly identified and presented in a concise and simple manner with illustrative and practical examples. Vibration concepts include a review of selected topics in mechanics; a description of single-degree-of-freedom (SDOF) systems in terms of equivalent mass, equivalent stiffness, and equivalent damping; a unified treatment of various forced response problems (base excitation and rotating balance); an introduction to systems thinking, highlighting the fact that SDOF analysis is a building block for multi-degree-of-freedom (MDOF) and continuous system analyses via modal analysis; and a simple introduction to finite element analysis to connect continuous system and MDOF analyses. There are more than 60 exercise problems, and a complete solutions manual. The use of MATLAB® software is emphasised.

1. Coverpage
2. Half title page
3. Title page
5. Dedication
6. Contents
7. Preface
8. 1 Equivalent Single-Degree-of-Freedom System and Free Vibration
1. 1.1 Degrees of Freedom
2. 1.2 Elements of a Vibratory System
1. 1.2.1 Mass and/or Mass-Moment of Inertia
2. 1.2.2 Spring
3. 1.2.3 Damper
3. 1.3 Equivalent Mass, Equivalent Stiffness, and Equivalent Damping Constant for an SDOF System
1. 1.3.1 A Rotor–Shaft System
2. 1.3.2 Equivalent Mass of a Spring
3. 1.3.3 Springs in Series and Parallel
4. 1.3.4 An SDOF System with Two Springs and Combined Rotational and Translational Motion
5. 1.3.5 Viscous Dampers in Series and Parallel
4. 1.4 Free Vibration of an Undamped SDOF System
1. 1.4.1 Differential Equation of Motion
2. 1.4.2 Solution of the Differential Equation of Motion Governing Free Vibration of an Undamped Spring–Mass System
5. 1.5 Free Vibration of a Viscously Damped SDOF System
1. 1.5.1 Differential Equation of Motion
2. 1.5.2 Solution of the Differential Equation of Motion Governing Free Vibration of a Damped Spring–Mass System
3. 1.5.3 Logarithmic Decrement: Identification of Damping Ratio from Free Response of an Underdamped System (0 < ξ < 1)
6. 1.6 Stability of an SDOF Spring–Mass–Damper System
7. Exercise Problems
9. 2 Vibration of a Single-Degree-of-Freedom System Under Constant and Purely Harmonic Excitation
1. 2.1 Responses of Undamped and Damped SDOF Systems to a Constant Force
2. 2.2 Response of an Undamped SDOF System to a Harmonic Excitation
3. 2.3 Response of a Damped SDOF System to a Harmonic Excitation
4. 2.4 Rotating Unbalance
5. 2.5 Base Excitation
6. 2.6 Vibration Measuring Instruments
7. 2.7 Equivalent Viscous Damping for Nonviscous Energy Dissipation
8. Exercise Problems
10. 3 Responses of an SDOF Spring–Mass–Damper System to Periodic and Arbitrary Forces
1. 3.1 Response of an SDOF System to a Periodic Force
2. 3.2 Response to an Excitation with Arbitrary Nature
1. 3.2.1 Unit Impulse Function δ(t − a)
2. 3.2.2 Unit Impulse Response of an SDOF System with Zero Initial Conditions
3. 3.2.3 Convolution Integral: Response to an Arbitrary Excitation with Zero Initial Conditions
4. 3.2.4 Convolution Integral: Response to an Arbitrary Excitation with Nonzero Initial Conditions
3. 3.3 Laplace Transformation
1. 3.3.1 Properties of Laplace Transformation
2. 3.3.2 Response of an SDOF System via Laplace Transformation
3. 3.3.3 Transfer Function and Frequency Response Function
4. Exercise Problems
11. 4 Vibration of Two-Degree-of-Freedom-Systems
1. 4.1 Mass, Stiffness, and Damping Matrices
2. 4.2 Natural Frequencies and Mode Shapes
3. 4.3 Free Response of an Undamped 2DOF System
4. 4.4 Forced Response of an Undamped 2DOF System Under Sinusoidal Excitation
5. 4.5 Free Vibration of a Damped 2DOF System
6. 4.6 Steady-State Response of a Damped 2DOF System Under Sinusoidal Excitation
7. 4.7 Vibration Absorber
1. 4.7.1 Undamped Vibration Absorber
2. 4.7.2 Damped Vibration Absorber
8. 4.8 Modal Decomposition of Response
9. Exercise Problems
12. 5 Finite and Infinite (Continuous) Dimensional Systems
1. 5.1 Multi-Degree-of-Freedom Systems
1. 5.1.1 Natural Frequencies and Modal Vectors (Mode Shapes)
2. 5.1.2 Orthogonality of Eigenvectors for Symmetric Mass and Symmetric Stiffness Matrices
3. 5.1.3 Modal Decomposition
2. 5.2 Continuous Systems Governed by Wave Equations
1. 5.2.1 Transverse Vibration of a String
2. 5.2.2 Longitudinal Vibration of a Bar
3. 5.2.3 Torsional Vibration of a Circular Shaft
3. 5.3 Continuous Systems: Transverse Vibration of a Beam
1. 5.3.1 Governing Partial Differential Equation of Motion
2. 5.3.2 Natural Frequencies and Mode Shapes
3. 5.3.3 Computation of Response
4. 5.4 Finite Element Analysis
1. 5.4.1 Longitudinal Vibration of a Bar
2. 5.4.2 Transverse Vibration of a Beam
5. Exercise Problems
13. Appendix A: Equivalent stiffnesses (spring constants) of beams, torsional shaft, and longitudinal bar
14. Appendix B: Some mathematical formulae
15. Appendix C: Laplace transform table
16. References
17. Index