Vibration Problems in Engineering [Hardcover]

The Fifth Edition of this classic work retains the most useful portions of Timoshenko's book on vibration theory and introduces powerful, modern computational techniques. The normal mode method is emphasized for linear multi-degree and infinite-degree-of-freedom systems and numerical methods dominate the approach to nonlinear systems. A new chapter on the finite-element method serves to show how any continuous system can be discretized for the purpose of simplifying the analysis. Includes revised problems, examples of applications and computer programs.

Preface xi

1 Systems with One Degree of Freedom 1

1.1 Examples of One-Degree Systems 1

1.2 Undamped Free Translational Vibrations 2

1.3 Rotational Vibrations 12

1.4 Energy Method 24

1.5 Rayleigh’s Method 24

1.6 Forced Vibrations: Steady State 39

1.7 Forced Vibrations with Viscous Damping 52

1.8 Free Vibrations with Viscous Damping 61

1.9 Forced Vibrations with Viscous Damping 61

1.10 Equivalent Viscous Damping 69

1.11 General Periodic Forcing Functions 76

1.12 Arbitrary Forcing Functions 84

1.13 Arbitrary Support Motions 93

1.14 Response Spectra 99

1.15 Step-by-Step Response Calculations 107

References 113

Problems 114

2 Systems with Nonlinear Characteristics 139

2.1 Examples of Nonlinear Systems 139

2.2 Direct Integration for Velocity and Period 149

2.3 Approximate Methods for Free Vló@