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Table of Contents
1 Cover
2 Preface
4 1 The Transition from Dynamics to Vibrations 1.1 Bead on a Wire: The Nonlinear Equations of Motion 1.2 Equilibrium Solutions 1.3 Linearization 1.4 Summary Exercises Notes
5 2 Single Degree of Freedom Systems – Modeling 2.1 Modeling Single Degree of Freedom Systems Exercises Notes
6 3 Single Degree of Freedom Systems – Free Vibrations 3.1 Undamped Free Vibrations 3.2 Response to Initial Conditions 3.3 Damped Free Vibrations 3.4 Root Locus Exercises Notes
7 4 SDOF Systems – Forced Vibrations – Response to Initial Conditions 4.1 Time Response to a Harmonically Applied Force in Undamped Systems Exercises
8 5 SDOF Systems – Steady State Forced Vibrations 5.1 Undamped Steady State Response to a Harmonically Applied Force 5.2 Damped Steady State Response to a Harmonically Applied Force 5.3 Response to Harmonic Base Motion 5.4 Response to a Rotating Unbalance 5.5 Accelerometers Exercises Notes
9 6 Damping 6.1 Linear Viscous Damping 6.2 Coulomb or Dry Friction Damping 6.3 Logarithmic Decrement Exercises Notes
10 7 Systems with More than One Degree of Freedom 7.1 2DOF Undamped Free Vibrations – Modeling 7.2 2DOF Undamped Free Vibrations – Natural Frequencies 7.3 2DOF Undamped Free Vibrations – Mode Shapes 7.4 Mode Shape Descriptions 7.5 Response to Initial Conditions 7.6 2DOF Undamped Forced Vibrations 7.7 Vibration Absorbers 7.8 The Method of Normal Modes 7.9 The Cart and Pendulum Example 7.10 Normal Modes Example Exercises Notes
11 8 Continuous Systems 8.1 The Equations of Motion for a Taut String 8.2 Natural Frequencies and Mode Shapes for a Taut String 8.3 Vibrations of Uniform Beams Exercises Notes
12 9 Finite Elements 9.1 Shape Functions 9.2 The Stiffness Matrix for an Elastic Rod 9.3 The Mass Matrix for an Elastic Rod 9.4 Using Multiple Elements 9.5 The Two‐noded Beam Element 9.6 Two‐noded Beam Element Vibrations Example Exercises Notes
13 10 The Inerter 10.1 Modeling the Inerter 10.2 The Inerter in the Equations of Motion 10.3 An Examination of the Effect of an Inerter on System Response 10.4 The Inerter as a Vibration Absorber