Mechanical Vibrations I

1.Modelling Vibrating Systems 5
1.1 Vibrations vs. Oscillations 5
1.2 Discrete vs. Continuous Systems 6
1.3 Simple Vibrating Systems 7
1.4 Vibratory Motions 8
1.5 Damping 10

2. Simple Linear Systems 11
2.1 Undamped Free Vibrations 11
2.2 Undamped Forced Vibrations 22
2.3 Damped Free Vibrations 35
2.4 Damped Forced Vibrations 42
Exercices 73

3. Simple Non-Linear Systems 79
3.1 Non-Linear Harmonic Response 79
3.2 Cubic Stiffness 81
3.3 Combined Coulomb and Structural Damping 92
3.4 Quadratic Damping 97
3.5 Effect of Pre-Loading 103

4 MECHANICAL VIBRATIONS
4. Two-Degree-of-Freedom Systems 105
4.1 Coupled Translation 106
4.2 Torsional Systems 119
4.3 Flexural Systems 130
4.4 Coupled Translation and Rotation 145
4.5 Coupled Pendulums 151
4.6 Damped Systems 156
Exercices 179

5. Several Degrees of Freedom 183
5.1 Lumped Mass Systems 184
5.2 Plane Trusses 210
5.3 Plane Frames 220
5.4 Grillages 234
5.5 Frequency Response Functions 241
Exercices 247

6. Continuous Systems 259
6.1 Lateral Vibrations of Thin Beams 259
6.2 Longitudinal Vibration of Rods 275
6.3 Torsional Vibration of Rods 278
6.4 Timoshenko Beams 280

References 281
Index 289