Mechanical Vibration and Shock Analysis, Second Edition Volume 2: Mechanical Shock
This volume considers the shock response spectrum, its various definitions, its properties, and the assumptions involved in its calculation. In developing the practical application of these concepts, the shock shapes or profiles most often used in test facilities are presented, together with their characteristics and indications of how to establish test configurations comparable with those of the real-world, measured environment. Following this analysis there is a case study of how to meet these specifications using standard laboratory equipment, shock machines, electrodynamic exciters driven by a time signal or a response spectrum. Discussion of the limitations, advantages and disadvantages of each method is presented.
The Mechanical Vibration and Shock Analysis five-volume series has been written with both the professional engineer and the academic in mind. Christian Lalanne explores every aspect of vibration and shock, two fundamental and extremely significant areas of mechanical engineering, from both a theoretical and practical point of view. The five volumes cover all the necessary issues in this area of mechanical engineering. The theoretical analyses are placed in the context of both the real world and the laboratory, which is essential for the development of specifications.
Author(s): Christian Lalanne
Edition: 2
Publisher: Wiley-ISTE
Year: 2009
Language: English
Pages: 421
Mechanical Shock......Page 5
Table of Contents......Page 7
Foreword to Series......Page 13
Introduction......Page 17
List of Symbols......Page 19
1.1.1. Shock......Page 23
1.1.2. Transient signal......Page 24
1.1.5. Half-sine shock......Page 25
1.1.6. Versed sine (or haversine) shock......Page 26
1.1.7. Terminal peak sawtooth (TPS) shock (or final peak sawtooth (FPS))......Page 27
1.1.8. Initial peak sawtooth (IPS) shock......Page 28
1.1.9. Square shock......Page 29
1.1.11. Decaying sinusoidal pulse......Page 30
1.1.13. Pyroshock......Page 31
1.3.1. Definition......Page 34
1.3.3. Fourier transforms of simple shocks......Page 36
1.3.4. What represents the Fourier transform of a shock?......Page 47
1.3.5. Importance of the Fourier transform......Page 49
1.4.1. Energy according to frequency......Page 50
1.5.2. Case: signal not yet digitized......Page 51
1.5.4. Adding zeros to the shock signal before the calculation of its Fourier transform......Page 54
1.6.1. Limit of the Fourier transform......Page 58
1.6.2. Short term Fourier transform (STFT)......Page 61
1.6.3. Wavelet transform......Page 66
2.1. Main principles......Page 73
2.2.1. Shock defined by a force......Page 77
2.2.3. Generalization......Page 78
2.2.4. Response of a one-degree-of-freedom system to simple shocks......Page 83
2.3.3. Relative displacement shock spectrum......Page 87
2.3.6. Secondary (or residual) SRS......Page 88
2.3.8. Negative (or maximum negative) SRS......Page 89
2.3.9. Maximax SRS......Page 90
2.4.1. Definition......Page 91
2.4.2. Half-sine pulse......Page 93
2.4.3. Versed sine pulse......Page 94
2.4.4. Terminal peak sawtooth pulse......Page 96
2.4.5. Initial peak sawtooth pulse......Page 97
2.4.7. Trapezoidal pulse......Page 99
2.5. Choice of the type of SRS......Page 100
2.6. Comparison of the SRS of the usual simple shapes......Page 101
2.7. SRS of a shock defined by an absolute displacement of the support......Page 102
2.8. Influence of the amplitude and the duration of the shock on its SRS......Page 103
2.10. Algorithms for calculation of the SRS......Page 104
2.11. Subroutine for the calculation of the SRS......Page 105
2.12. Choice of the sampling frequency of the signal......Page 108
2.13. Example of use of the SRS......Page 112
2.14. Use of SRS for the study of systems with several degrees of freedom......Page 114
3.1. Shock response spectra domains......Page 117
3.2.2. Shocks with zero velocity change......Page 118
3.2.3. Shocks with ΔV = 0 and ΔD ≠ 0 at the end of a pulse......Page 127
3.2.4. Shocks with ΔV = 0 and ΔD = 0 at the end of a pulse......Page 130
3.2.5. Notes on residual spectrum......Page 132
3.3. Properties of SRS at high frequencies......Page 133
3.5. Choice of damping......Page 136
3.8. Charts......Page 140
3.9.1. Primary SRS and Fourier transform......Page 142
3.9.2. Residual SRS and Fourier transform......Page 144
3.9.3. Comparison of the relative severity of several shocks using their Fourier spectra and their shock response spectra......Page 147
3.10.1. Main sources of errors......Page 151
3.10.2. Influence of background noise of the measuring equipment......Page 152
3.10.3. Influence of zero shift......Page 154
3.11. Use of the SRS for pyroshocks......Page 157
4.1. Introduction......Page 161
4.2. Simplification of the measured signal......Page 162
4.3.1. Synthesis of spectra......Page 164
4.3.3. Choice of shape......Page 166
4.3.5. Duration......Page 168
4.3.6. Difficulties......Page 172
4.4. Other methods......Page 173
4.4.1. Use of a swept sine......Page 174
4.4.2. Simulation of SRS using a fast swept sine......Page 175
4.4.3. Simulation by modulated random noise......Page 179
4.4.4. Simulation of a shock using random vibration......Page 180
4.4.5. Least favorable response technique......Page 181
4.4.6. Restitution of an SRS by a series of modulated sine pulses......Page 182
4.5. Interest behind simulation of shocks on shaker using a shock spectrum......Page 184
5.2.1. General expressions of the shock motion......Page 189
5.2.2. Impulse mode......Page 192
5.2.3. Impact mode......Page 193
5.3. Versed sine pulse......Page 203
5.4. Square pulse......Page 205
5.5. Terminal peak sawtooth pulse......Page 208
5.6. Initial peak sawtooth pulse......Page 210
6.1. Main types......Page 213
6.2. Impact shock machines......Page 215
6.3.1. Lightweight high impact shock machine......Page 225
6.3.2. Medium weight high impact shock machine......Page 226
6.4. Pneumatic machines......Page 227
6.5. Specific testing facilities......Page 229
6.6.1. Half-sine pulse......Page 230
6.6.2. TPS shock pulse......Page 238
6.6.3. Square pulse – trapezoidal pulse......Page 245
6.6.4. Universal shock programmer......Page 246
7.1. Principle behind the generation of a signal with a simple shape versus time......Page 255
7.2. Main advantages of the generation of shock using shakers......Page 256
7.3.1. Mechanical limitations......Page 257
7.3.2. Electronic limitations......Page 258
7.5.1. Requirements......Page 259
7.5.2. Pre-shock or post-shock......Page 260
7.5.3. Kinematics of the movement for symmetric pre- and post-shock......Page 264
7.5.4. Kinematics of the movement for a pre-shock or post-shock alone......Page 275
7.5.5. Abacuses......Page 277
7.5.6. Influence of the shape of pre- and post-pulses......Page 278
7.5.7. Optimized pre- and post-shocks......Page 281
7.6.2. Influence of the pre- and post-shocks on the time history response of a one-degree-of-freedom system......Page 286
7.6.3. Incidence on the shock response spectrum......Page 288
8.1.1. Problems......Page 293
8.1.2. Parallel filter method......Page 294
8.1.3. Current numerical methods......Page 295
8.2.1. Definition......Page 300
8.2.2. Response spectrum......Page 301
8.2.3. Velocity and displacement......Page 304
8.2.4. Constitution of the total signal......Page 305
8.2.5. Methods of signal compensation......Page 306
8.2.6. Iterations......Page 312
8.3.2. Velocity and displacement......Page 314
8.4.1. Definition......Page 316
8.4.2. Velocity and displacement......Page 317
8.4.3. Comparison of ZERD waveform with standard decaying sinusoid......Page 319
8.4.4. Reduced response spectra......Page 320
8.5.1. Definition......Page 321
8.5.2. Velocity and displacement......Page 322
8.5.3. Response of a one-degree-of-freedom system......Page 324
8.5.4. Response spectrum......Page 327
8.5.5. Time history synthesis from shock spectrum......Page 328
8.6.1. Definition......Page 329
8.6.2. Velocity and displacement......Page 332
8.6.3. Response spectrum......Page 333
8.6.4. Time history synthesis from shock spectrum......Page 334
8.7. Comparison of WAVSIN, SHOC waveforms and decaying sinusoid......Page 335
8.8. Use of a fast swept sine......Page 336
8.9. Problems encountered during the synthesis of the waveforms......Page 339
8.10. Criticism of control by SRS......Page 341
8.11.1. IES proposal......Page 345
8.11.2. Specification of a complementary parameter......Page 346
8.12.1. C.D. Robbins and E.P. Vaughan's method......Page 351
8.12.2. Evaluation of the necessary force, power and stroke......Page 353
9.1. Simulations using pyrotechnic facilities......Page 359
9.2. Simulation using metal to metal impact......Page 363
9.4. Simulation using conventional shock machines......Page 364
Appendix: Similitude in Mechanics......Page 367
Mechanical Shock Tests: A Brief Historical Background......Page 371
Bibliography......Page 373
Index......Page 387
Summary of other Volumes in the Series......Page 391
