Cover -- Title Page -- Contents -- Foreword to Series -- Introduction -- List of Symbols -- Chapter 1. Shock Analysis -- 1.1. Definitions -- 1.1.1. Shock -- 1.1.2. Transient signal -- 1.1.3. Jerk -- 1.1.4. Simple (or perfect) shock -- 1.1.5. Half-sine shock -- 1.1.6. Versed sine (or haversine) shock -- 1.1.7. Terminal peak sawtooth (TPS) shock (or final peak sawtooth (FPS)) -- 1.1.8. Initial peak sawtooth (IPS) shock -- 1.1.9. Square shock -- 1.1.10. Trapezoidal shock -- 1.1.11. Decaying sinusoidal pulse -- 1.1.12. Bump test -- 1.1.13. Pyroshock -- 1.2. Analysis in the time domain -- 1.3. Temporal moments -- 1.4. Fourier transform -- 1.4.1. Definition -- 1.4.2. Reduced Fourier transform -- 1.4.3. Fourier transforms of simple shocks -- 1.4.4. What represents the Fourier transform of a shock? -- 1.4.5. Importance of the Fourier transform -- 1.5. Energy spectrum -- 1.5.1. Energy according to frequency -- 1.5.2. Average energy spectrum -- 1.6. Practical calculations of the Fourier transform -- 1.6.1. General -- 1.6.2. Case: signal not yet digitized -- 1.6.3. Case: signal already digitized -- 1.6.4. Adding zeros to the shock signal before the calculation of its Fourier transform -- 1.6.5. Windowing -- 1.7. The interest of time-frequency analysis -- 1.7.1. Limit of the Fourier transform -- 1.7.2. Short term Fourier transform (STFT) -- 1.7.3. Wavelet transform -- Chapter 2. Shock Response Spectrum -- 2.1. Main principles -- 2.2. Response of a linear one-degree-of-freedom system -- 2.2.1. Shock defined by a force -- 2.2.2. Shock defined by an acceleration -- 2.2.3. Generalization -- 2.2.4. Response of a one-degree-of-freedom system to simple shocks -- 2.3. Definitions -- 2.3.1. Response spectrum -- 2.3.2. Absolute acceleration SRS -- 2.3.3. Relative displacement shock spectrum -- 2.3.4. Primary (or initial) positive SRS.

2.3.5. Primary (or initial) negative SRS -- 2.3.6. Secondary (or residual) SRS -- 2.3.7. Positive (or maximum positive) SRS -- 2.3.8. Negative (or maximum negative) SRS -- 2.3.9. Maximax SRS -- 2.4. Standardized response spectra -- 2.4.1. Definition -- 2.4.2. Half-sine pulse -- 2.4.3. Versed sine pulse -- 2.4.4. Terminal peak sawtooth pulse -- 2.4.5. Initial peak sawtooth pulse -- 2.4.6. Square pulse -- 2.4.7. Trapezoidal pulse -- 2.5. Choice of the type of SRS -- 2.6. Comparison of the SRS of the usual simple shapes -- 2.7. SRS of a shock defined by an absolute displacement of the support -- 2.8. Influence of the amplitude and the duration of the shock on its SRS -- 2.9. Difference between SRS and extreme response spectrum (ERS) -- 2.10. Algorithms for calculation of the SRS -- 2.11. Subroutine for the calculation of the SRS -- 2.12. Choice of the sampling frequency of the signal -- 2.13. Example of use of the SRS -- 2.14. Use of SRS for the study of systems with several degrees of freedom -- 2.15. Damage boundary curve -- Chapter 3. Properties of Shock Response Spectra -- 3.1. Shock response spectra domains -- 3.2. Properties of SRS at low frequencies -- 3.2.1. General properties -- 3.2.2. Shocks with zero velocity change -- 3.2.3. Shocks with ΔV = 0 and ΔD ≠ 0 at the end of a pulse -- 3.2.4. Shocks with ΔV = 0 and ΔD = 0 at the end of a pulse -- 3.2.5. Notes on residual spectrum -- 3.3. Properties of SRS at high frequencies -- 3.4. Damping influence -- 3.5. Choice of damping -- 3.6. Choice of frequency range -- 3.7. Choice of the number of points and their distribution -- 3.8. Charts -- 3.9. Relation of SRS with Fourier spectrum -- 3.9.1. Primary SRS and Fourier transform -- 3.9.2. Residual SRS and Fourier transform -- 3.9.3. Comparison of the relative severity of several shocks using their Fourier spectra and their shock response spectra.

3.10. Care to be taken in the calculation of the spectra -- 3.10.1. Main sources of errors -- 3.10.2. Influence of background noise of the measuring equipment -- 3.10.3. Influence of zero shift -- 3.11. Specific case of pyroshocks -- 3.11.1. Acquisition of the measurements -- 3.11.2. Examination of the signal before calculation of the SRS -- 3.11.3. Examination of the SRS -- 3.12. Pseudo-velocity shock spectrum -- 3.12.1. Hunt's relationship -- 3.12.2. Interest of PVSS -- 3.13. Use of the SRS for pyroshocks -- 3.14. Other propositions of spectra -- 3.14.1. Pseudo-velocity calculated from the energy transmitted -- 3.14.2. Pseudo-velocity from the "input" energy at the end of a shock -- 3.14.3. Pseudo-velocity from the unit "input" energy -- 3.14.4. SRS of the "total" energy -- Chapter 4. Development of Shock Test Specifications -- 4.1. Introduction -- 4.2. Simplification of the measured signal -- 4.3. Use of shock response spectra -- 4.3.1. Synthesis of spectra -- 4.3.2. Nature of the specification -- 4.3.4. Amplitude -- 4.3.5. Duration -- 4.3.6. Difficulties -- 4.4. Other methods -- 4.4.1. Use of a swept sine -- 4.4.2. Simulation of SRS using a fast swept sine -- 4.4.3. Simulation by modulated random noise -- 4.4.4. Simulation of a shock using random vibration -- 4.4.5. Least favorable response technique -- 4.4.6. Restitution of an SRS by a series of modulated sine pulses -- 4.5. Interest behind simulation of shocks on shaker using a shock spectrum -- Chapter 5. Kinematics of Simple Shocks -- 5.1. Introduction -- 5.2. Half-sine pulse -- 5.2.1. General expressions of the shock motion -- 5.2.2. Impulse mode -- 5.2.3. Impact mode -- 5.3. Versed sine pulse -- 5.4. Square pulse -- 5.5. Terminal peak sawtooth pulse -- 5.6. Initial peak sawtooth pulse -- Chapter 6. Standard Shock Machines -- 6.1. Main types -- 6.2. Impact shock machines.

6.3. High impact shock machines -- 6.3.1. Lightweight high impact shock machine -- 6.3.2. Medium weight high impact shock machine -- 6.4. Pneumatic machines. -- 6.5. Specific testing facilities -- 6.6. Programmers -- 6.6.1. Half-sine pulse -- 6.6.2. TPS shock pulse -- 6.6.3. Square pulse - trapezoidal pulse -- 6.6.4. Universal shock programmer -- Chapter 7. Generation of Shocks Using Shakers -- 7.1. Principle behind the generation of a signal with a simple shape versus time -- 7.2. Main advantages of the generation of shock using shakers -- 7.3. Limitations of electrodynamic shakers -- 7.3.1. Mechanical limitations -- 7.3.2. Electronic limitations -- 7.4. Remarks on the use of electrohydraulic shakers -- 7.5. Pre- and post-shocks -- 7.5.1. Requirements -- 7.5.2. Pre-shock or post-shock -- 7.5.3. Kinematics of the movement for symmetric pre- and post-shock -- 7.5.4. Kinematics of the movement for a pre-shock or a post-shock alone -- 7.5.5. Abacuses -- 7.5.6. Influence of the shape of pre- and post-pulses -- 7.5.7. Optimized pre- and post-shocks -- 7.6. Incidence of pre- and post-shocks on the quality of simulation -- 7.6.1. General -- 7.6.2. Influence of the pre- and post-shocks on the time history response of a one-degree-of-freedom system -- 7.6.3. Incidence on the shock response spectrum -- Chapter 8. Control of a Shaker Using a Shock Response Spectrum -- 8.1. Principle of control using a shock response spectrum -- 8.1.1. Problems -- 8.1.2. Parallel filter method -- 8.1.3. Current numerical methods -- 8.2. Decaying sinusoid -- 8.2.1. Definition -- 8.2.2. Response spectrum -- 8.2.3. Velocity and displacement -- 8.2.4. Constitution of the total signal -- 8.2.5. Methods of signal compensation -- 8.2.6. Iterations -- 8.3. D.L. Kern and C.D. Hayes' function -- 8.3.1. Definition -- 8.3.2. Velocity and displacement -- 8.4. ZERD function.

8.4.1. Definition -- 8.4.2. Velocity and displacement -- 8.4.3. Comparison of ZERD waveform with standard decaying sinusoid -- 8.4.4. Reduced response spectra -- 8.5. WAVSIN waveform -- 8.5.1. Definition -- 8.5.2. Velocity and displacement -- 8.5.3. Response of a one-degree-of-freedom system -- 8.5.4. Response spectrum -- 8.5.5. Time history synthesis from shock spectrum -- 8.6. SHOC waveform -- 8.6.1. Definition -- 8.6.2. Velocity and displacement -- 8.6.3. Response spectrum -- 8.6.4. Time history synthesis from shock spectrum -- 8.7. Comparison of WAVSIN, SHOC waveforms and decaying sinusoid -- 8.8. Waveforms based on the cosm(x) window -- 8.9. Use of a fast swept sine -- 8.10. Problems encountered during the synthesis of the waveforms -- 8.11. Criticism of control by SRS -- 8.12. Possible improvements -- 8.12.1. IES proposal -- 8.12.2. Specification of a complementary parameter -- 8.12.3. Remarks on the properties of the response spectrum -- 8.13. Estimate of the feasibility of a shock specified by its SRS -- 8.13.1. C.D. Robbins and E.P. Vaughan's method -- 8.13.2. Evaluation of the necessary force, power and stroke -- Chapter 9. Simulation of Pyroshocks -- 9.1. Simulations using pyrotechnic facilities -- 9.2. Simulation using metal to metal impact -- 9.3. Simulation using electrodynamic shakers -- 9.4. Simulation using conventional shock machines -- Appendix. Similitude in Mechanics -- A1. Conservation of materials -- A2. Conservation of acceleration and stress -- Mechanical Shock Tests: A Brief Historical Background -- Bibliography -- Index -- Summary of other Volumes in the series.