Fundamentals of Mechanical Vibrations

Title Page
Copyright
Table of Contents
Series Preface
Preface
Chapter 1: A Crash Course on Lagrangian Dynamics
	1.1 Objectives
	1.2 Concept of “Equation of Motion”
	1.3 Generalized Coordinates
	1.4 Admissible Variations
	1.5 Degrees of Freedom
	1.6 Virtual Work and Generalized Forces
	1.7 Lagrangian
	1.8 Lagrange's Equation
	1.9 Procedure for Deriving Equation(s) of Motion
	1.10 Worked Examples
	1.11 Linearization of Equations of Motion
	1.12 Chapter Summary
	Problems
Chapter 2: Vibrations of Single-DOF Systems
	2.1 Objectives
	2.2 Types of Vibration Analyses
	2.3 Free Vibrations of Undamped System
	2.4 Free Vibrations of Damped Systems
	2.5 Using Normalized Equation of Motion
	2.6 Forced Vibrations I: Steady-State Responses
	2.7 Forced Vibrations II: Transient Responses
	2.8 Chapter Summary
	Problems
Chapter 3: Lumped-Parameter Modeling
	3.1 Objectives
	3.2 Modeling
	3.3 Idealized Elements
	3.4 Lumped-Parameter Modeling of Simple Components and Structures
	3.5 Alternative Methods
	3.6 Examples with Lumped-Parameter Models
	3.7 Chapter Summary
	Problems
Chapter 4: Vibrations of Multi-DOF Systems
	4.1 Objectives
	4.2 Matrix Equation of Motion
	4.3 Modal Analysis: Natural Frequencies and Mode Shapes
	4.4 Free Vibrations
	4.5 Eigenvalues and Eigenvectors
	4.6 Coupling, Decoupling, and Principal Coordinates
	4.7 Forced Vibrations I: Steady-State Responses
	4.8 Forced Vibrations II: Transient Responses
	4.9 Chapter Summary
	Problems
	Reference
Chapter 5: Vibration Analyses Using Finite Element Method
	5.1 Objectives
	5.2 Introduction to Finite Element Method
	5.3 Finite Element Analyses of Beams
	5.4 Vibration Analyses Using SOLIDWORKS
	5.5 Chapter Summary
	Problems
Appendix A: Review of Newtonian Dynamics
	A.1 Kinematics
	A.2 Kinetics
Appendix B: A Primer on MATLAB
	B.1 Matrix Computations
	B.2 Plotting
Appendix C: Tables of Laplace Transform
	C.1 Properties of Laplace Transform
	C.2 Function Transformations
Index
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