Vibration Problems in Engineering

Vibration Problems in Engineering
BY S. TIMOSHENKO
Professor of Theoretical and Engineering Mechanics
Stanford University
CONTENTS
CHAPTER I
PAGE
HARMONIC VIBRATIONS OF SYSTEMS HAVINO ONE DEGREE OF FREEDOM
. Free Harmonic Vibrations 1
2. Torsional Vibration 4
3. Forced Vibrations 8
4. Instruments for Investigating Vibrations 19
5. Spring Mounting of Machines 24
6. Other Technical Applications 26
/V. Damping 30
^78. Free Vibration with Viscous Damping 32
9. Forced Vibrations with Viscous Damping 38
10. Spring Mounting of Machines with Damping Considered 51
11. Free Vibrations with Coulomb’s Damping 54
12. Forced Vibrations with Coulomb’s Damping and other Kinds of Damping. 57
13. Machines for Balancing 62
14. General Case of Disturbing Force 64
v/15. Application of Equation of Energy in Vibration Problems 74
16. Rayleigh Method 83
17. Critical Speed of a Rotating Shaft 92
18. General Case of Disturbing Force 98
19. Effect of Low
Spots on Deflection of Rails 107
20. Self-Excited Vibration 110
CHAPTER IT
VIBRATION OF SYSTEMS WITH NON-LINEAR CHARACTERISTICS
21 . Examples of Non-Linear Systems 114
22. Vibrations of Systems with Non-linear Restoring Force 119
23. Graphical Solution 121
24. Numerical Solution 126
25. Method of Successive Approximations Applied to Free Vibrations 129
26. Forced Non-Linear Vibrations 137
CHAPTER 111
SYSTEMS WITH VARIABLE SPRING CHARACTERISTICS
27. Examples of Variable Spring Characteristics 151
28. Discussion of the Equation of Vibratory Motion with Variable Spring
Characteristics 160
29. Vibrations in the Side Rod Drive System of Electric Locomotives 167
viivia CONTENTS
CHAPTER IV
PAGE
SYSTEMS HAVING SEVERAL DEGREES OF FREEDOM
30. d’Alembert’s Principle and the Principle of Virtual Displacements 182
31. Generalized Coordinates and Generalized Forces 185
32. Lagrange’s Equations 189
33. The Spherical Pendulum 192
34. Free Vibrations. General Discussion 194
35. Particular Cases 206
36. Forced Vibrations 208
37. Vibration with Viscous Damping 213
38. Stability of Motion 216
39. Whirling of a Rotating Shaft Caused by Hysteresis 222
40. Vibration of Vehicles 229
41. Damping Vibration Absorber 240
CHAPTER V
TORSIONAL AND LATERAL VIBRATION OF SHAFTS
42. Free Torsional Vibrations of Shafts 253
43. Approximate Methods of Calculating Frequencies of Natural Vibrations . . 258
44. Forced Torsional Vibration of a Shaft with Several Discs 265
45. Torsional Vibration of Diesel Engine Crankshafts 270
46. Damper with Solid Friction 274
47. Lateral Vibrations of Shafts on Many Supports 277
48. Gyroscopic Effects on the Critical Speeds of Rotating Shafts 290
49. Effect of Weight of Shaft and Discs on the Critical Speed 299
50. Effect of Flexibility of Shafts on the Balancing of Machines 303
CHAPTER VI
VIBRATION OF ELASTIC BODIES
51. Longitudinal Vibrations of Prismatical Bars 307
52. Vibration of a Bar with a Load at the End 317
53. Torsional Vibration of Circular Shafts 325
54. Lateral Vibration of Prismatical Bars 331
55. The Effect of Shearing Force and Rotatory Inertia 337
V
56. Free Vibration of a Bar with Hinged Ends 338
Jbl. Other End Fastenings 342
>/58. Forced Vibration of a Beam with Supported Ends 348
59. Vibration of Bridges 358
60. Effect of Axial Forces on Lateral Vibrations 364
61. Vibration of Beams on Elastic Foundation 368
62. Ritz Method 370
63. Vibration of Bars of Variable Cross Section 376
64. Vibration of Turbine Blades . . . . . . 382CONTENTS ix
PAGE
65. Vibration of Hulls of Ships 388
06. Lateral Impact of Bars 392
67. Longitudinal Impact of Prismatical Bars 397
*8. Vibration of a Circular Ring 405
’69. Vibration of Membranes 411
70. Vibration of Plates 421
71. Vibration of Turbine Discs 435
APPENDIX
VIBRATION MEASURING INSTRUMENTS
1. General 443
2. Frequency Measuring Instruments 443
3. The Measurement of Amplitudes 444
4. Seismic Vibrographs 448
5. Torsiograph 452
6. Torsion Meters 453
7. Strain Recorders 457
AUTHOR INDEX 463
SUBJECT INDEX
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