Mechanical Vibration and Shock Analysis Volume 2: Mechanical Shock

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9781118931127.fmatter......Page 2
Title Page......Page 3
Copyright......Page 4
Table of Contents......Page 5
Foreword to Series......Page 12
Introduction......Page 16
List of Symbols......Page 18
1.1.1. Shock......Page 21
1.1.2. Transient signal......Page 22
1.1.5. Half-sine shock......Page 23
1.1.6. Versed sine (or haversine) shock......Page 24
1.1.7. Terminal peak sawtooth (TPS) shock (or final peak sawtooth (FPS))......Page 25
1.1.8. Initial peak sawtooth (IPS) shock......Page 26
1.1.9. Square shock......Page 27
1.1.11. Decaying sinusoidal pulse......Page 28
1.1.13. Pyroshock......Page 29
1.3. Temporal moments......Page 32
1.4.1. Definition......Page 35
1.4.3.1. Half-sine pulse......Page 37
1.4.3.2. Versed sine pulse......Page 38
1.4.3.3. TPS pulse......Page 39
1.4.3.4. IPS pulse......Page 41
1.4.3.5. Arbitrary triangular pulse......Page 43
1.4.3.6. Square pulse......Page 45
1.4.3.7. Trapezoidal pulse......Page 46
1.4.4. What represents the Fourier transform of a shock?......Page 49
1.4.5. Importance of the Fourier transform......Page 51
1.5.1. Energy according to frequency......Page 52
1.6.2. Case: signal not yet digitized......Page 53
1.6.3. Case: signal already digitized......Page 56
1.6.4. Adding zeros to the shock signal before the calculation of its Fourier transform......Page 57
1.6.5. Windowing......Page 60
1.7.1. Limit of the Fourier transform......Page 61
1.7.2. Short term Fourier transform (STFT)......Page 64
1.7.3. Wavelet transform......Page 69
2.1. Main principles......Page 75
2.2.1. Shock defined by a force......Page 79
2.2.3. Generalization......Page 80
2.2.4. Response of a one-degree-of-freedom system to simple shocks......Page 85
2.3.2. Absolute acceleration SRS......Page 89
2.3.5. Primary (or initial) negative SRS......Page 90
2.3.8. Negative (or maximum negative) SRS......Page 91
2.3.9. Maximax SRS......Page 92
2.4.1. Definition......Page 93
2.4.2. Half-sine pulse......Page 95
2.4.3. Versed sine pulse......Page 96
2.4.4. Terminal peak sawtooth pulse......Page 98
2.4.5. Initial peak sawtooth pulse......Page 99
2.4.7. Trapezoidal pulse......Page 101
2.5. Choice of the type of SRS......Page 102
2.6. Comparison of the SRS of the usual simple shapes......Page 103
2.8. Influence of the amplitude and the duration of the shock on its SRS......Page 104
2.11. Subroutine for the calculation of the SRS......Page 106
2.12. Choice of the sampling frequency of the signal......Page 110
2.13. Example of use of the SRS......Page 114
2.14. Use of SRS for the study of systems with several degrees of freedom......Page 116
2.15. Damage boundary curve......Page 120
3.1. Shock response spectra domains......Page 123
3.2.2. Shocks with zero velocity change......Page 124
3.2.3. Shocks with Δ V = 0 and Δ D ≠ 0 at the end of a pulse......Page 135
3.2.4. Shocks with Δ V = 0 and Δ D = 0 at the end of a pulse......Page 137
3.2.5. Notes on residual spectrum......Page 140
3.3. Properties of SRS at high frequencies......Page 141
3.5. Choice of damping......Page 144
3.6. Choice of frequency range......Page 147
3.7. Choice of the number of points and their distribution......Page 148
3.8. Charts......Page 151
3.9.1. Primary SRS and Fourier transform......Page 154
3.9.2. Residual SRS and Fourier transform......Page 156
3.9.3. Comparison of the relative severity of several shocks using their Fourier spectra and their shock response spectra......Page 159
3.10.2. Influence of background noise of the measuring equipment......Page 163
3.10.3. Influence of zero shift......Page 165
3.11.1. Acquisition of the measurements......Page 172
3.11.2. Examination of the signal before calculation of the SRS......Page 174
3.11.3. Examination of the SRS......Page 175
3.12.1. Hunt’s relationship......Page 176
3.12.2.1. Comparison of the severity of several shocks......Page 180
3.12.2.2. Estimation of the stress created in a structure......Page 181
3.13. Use of the SRS for pyroshocks......Page 182
3.14.2. Pseudo-velocity from the “input” energy at the end of a shock......Page 185
3.14.4. SRS of the “total” energy......Page 187
4.1. Introduction......Page 194
4.2. Simplification of the measured signal......Page 195
4.3.1. Synthesis of spectra......Page 197
4.3.2. Nature of the specification......Page 199
4.3.3. Choice of shape......Page 200
4.3.5. Duration......Page 201
4.3.6. Difficulties......Page 205
4.4. Other methods......Page 206
4.4.1. Use of a swept sine......Page 207
4.4.2. Simulation of SRS using a fast swept sine......Page 208
4.4.3. Simulation by modulated random noise......Page 212
4.4.4. Simulation of a shock using random vibration......Page 213
4.4.5. Least favorable response technique......Page 214
4.4.6. Restitution of an SRS by a series of modulated sine pulses......Page 215
4.5. Interest behind simulation of shocks on shaker using a shock spectrum......Page 217
5.2.1. General expressions of the shock motion......Page 221
5.2.2. Impulse mode......Page 224
5.2.3.1. General case......Page 225
5.2.3.2. Impact without rebound......Page 226
5.2.3.3. Velocity of rebound equal and opposite to the velocity of impact (perfect rebound)......Page 228
5.2.3.4. Velocity of rebound equal and opposed to half of the impact velocity......Page 230
5.2.3.5. Summary chart: remarks on the general case of an arbitrary rebound velocity......Page 231
5.2.3.6. Locus of the maxima......Page 233
5.3. Versed sine pulse......Page 234
5.4. Square pulse......Page 236
5.5. Terminal peak sawtooth pulse......Page 239
5.6. Initial peak sawtooth pulse......Page 241
6.1. Main types......Page 243
6.2. Impact shock machines......Page 245
6.3.1. Lightweight high impact shock machine......Page 255
6.3.2. Medium weight high impact shock machine......Page 256
6.4. Pneumatic machines......Page 257
6.5. Specific testing facilities......Page 259
6.6.1. Half-sine pulse......Page 260
6.6.2. TPS shock pulse......Page 268
6.6.4. Universal shock programmer......Page 276
6.6.4.2. Generation of a TPS shock pulse......Page 277
6.6.4.4. Limitations......Page 278
7.1. Principle behind the generation of a signal with a simple shape versus time......Page 284
7.2. Main advantages of the generation of shock using shakers......Page 285
7.3.1. Mechanical limitations......Page 286
7.5.1. Requirements......Page 288
7.5.2. Pre-shock or post-shock......Page 290
7.5.3.1. Half-sine pulse......Page 293
7.5.3.2. Terminal sawtooth pulse......Page 301
7.5.3.4. Initial peak sawtooth pulse......Page 302
7.5.4. Kinematics of the movement for a pre-shock or a post-shock alone......Page 303
7.5.5. Abacuses......Page 305
7.5.6. Influence of the shape of pre- and post-pulses......Page 306
7.5.7. Optimized pre- and post-shocks......Page 309
7.6.2. Influence of the pre- and post-shocks on the time history response of a one degree-of-freedom system......Page 314
7.6.3. Incidence on the shock response spectrum......Page 317
8.1.1. Problems......Page 320
8.1.2. Parallel filter method......Page 321
8.1.3. Current numerical methods......Page 322
8.2.1. Definition......Page 327
8.2.2. Response spectrum......Page 328
8.2.3. Velocity and displacement......Page 331
8.2.4. Constitution of the total signal......Page 332
8.2.5. Methods of signal compensation......Page 333
8.2.6. Iterations......Page 340
8.3.1. Definition......Page 341
8.3.2. Velocity and displacement......Page 342
8.4.1.1. D.K. Fisher and M.R. Posehn expression......Page 343
8.4.1.2. D.O. Smallwood expression......Page 344
8.4.2. Velocity and displacement......Page 345
8.4.4.1. Influence of the damping η of the signal......Page 347
8.4.4.2. Influence of the Q factor......Page 348
8.5.1. Definition......Page 349
8.5.2. Velocity and displacement......Page 350
8.5.3. Response of a one-degree-of-freedom system......Page 352
8.5.3.1. Relative response displacement......Page 353
8.5.3.2. Absolute response acceleration......Page 354
8.5.4. Response spectrum......Page 355
8.5.5. Time history synthesis from shock spectrum......Page 356
8.6.1. Definition......Page 357
8.6.2. Velocity and displacement......Page 359
8.6.3.1. Influence of damping η of the signal......Page 360
8.6.3.2. Influence of Q factor on the spectrum......Page 361
8.6.4. Time history synthesis from shock spectrum......Page 362
8.8. Waveforms based on the cosm(x) window......Page 363
8.9. Use of a fast swept sine......Page 365
8.10. Problems encountered during the synthesis of the waveforms......Page 368
8.11. Criticism of control by SRS......Page 370
2. Require SRS at two different values of damping......Page 374
8.12.2.1. Rms duration of the shock......Page 375
8.12.2.3. Rms value of the signal......Page 377
8.12.2.4. Rms value in the frequency domain......Page 378
8.12.2.6. Use of the fatigue damage spectrum......Page 379
8.13.1. C.D. Robbins and E.P. Vaughan’s method......Page 380
8.13.2. Evaluation of the necessary force, power and stroke......Page 382
9.1. Simulations using pyrotechnic facilities......Page 388
9.2. Simulation using metal to metal impact......Page 392
9.3. Simulation using electrodynamic shakers......Page 394
9.4. Simulation using conventional shock machines......Page 395
A1. Conservation of materials......Page 398
A2. Conservation of acceleration and stress......Page 400
Mechanical Shock Tests: A Brief Historical Background......Page 402
Bibliography......Page 404
Index......Page 423
Summary of Other Volumes in the Series......Page 428
Summary of Volume 1 Sinusoidal Vibration......Page 429
Summary of Volume 3 Random Vibration......Page 435
Summary of Volume 4 Fatigue Damage......Page 443
Summary of Volume 5 Specification Development......Page 450