Cover -- Title Page -- Copyright -- Contents -- Foreword to Series -- Introduction -- List of Symbols -- Chapter 1. Extreme Response Spectrum of a Sinusoidal Vibration -- 1.1. The effects of vibration -- 1.2. Extreme response spectrum of a sinusoidal vibration -- 1.2.1. Definition -- 1.2.2. Case of a single sinusoid -- 1.2.3. General case -- 1.2.4. Case of a periodic signal -- 1.2.5. Case of n harmonic sinusoids -- 1.2.6. Influence of the dephasing between the sinusoids -- 1.3. Extreme response spectrum of a swept sine vibration -- 1.3.1. Sinusoid of constant amplitude throughout the sweeping process -- 1.3.2. Swept sine composed of several constant levels -- Chapter 2. Extreme Response Spectrum of a Random Vibration -- 2.1. Unspecified vibratory signal -- 2.2. Gaussian stationary random signal -- 2.2.1. Calculation from peak distribution -- 2.2.2. Use of the largest peak distribution law -- 2.2.3. Response spectrum defined by k times the rms response -- 2.2.4. Other ERS calculation methods -- 2.3. Limit of the ERS at the high frequencies -- 2.4. Response spectrum with up-crossing risk -- 2.4.1. Complete expression -- 2.4.2. Approximate relation -- 2.4.3. Approximate relation URS - PSD -- 2.4.4. Calculation in a hypothesis of independence of threshold overshoot -- 2.4.5. Use of URS -- 2.5. Comparison of the various formulae -- 2.6. Effects of peak truncation on the acceleration time history -- 2.6.1. Extreme response spectra calculated from the time history signal -- 2.6.2. Extreme response spectra calculated from the power spectral densities -- 2.6.3. Comparison of extreme response spectra calculated from time history signals and power spectral densities -- 2.7. Sinusoidal vibration superimposed on a broadband random vibration -- 2.7.1. Real environment -- 2.7.2. Case of a single sinusoid superimposed to a wideband noise.

2.7.3. Case of several sinusoidal lines superimposed on a broadband random vibration -- 2.8. Swept sine superimposed on a broadband random vibration -- 2.8.1. Real environment -- 2.8.2. Case of a single swept sine superimposed to a wideband noise -- 2.8.3. Case of several swept sines superimposed on a broadband random vibration -- 2.9. Swept narrowbands on a wideband random vibration -- 2.9.1. Real environment -- 2.9.2. Extreme response spectrum -- Chapter 3. Fatigue Damage Spectrum of a Sinusoidal Vibration -- 3.1. Fatigue damage spectrum definition -- 3.2. Fatigue damage spectrum of a single sinusoid -- 3.3. Fatigue damage spectrum of a periodic signal -- 3.4. General expression for the damage -- 3.5. Fatigue damage with other assumptions on the S-N curve -- 3.5.1. Taking account of fatigue limit -- 3.5.2. Cases where the S-N curve is approximated by a straight line in log-lin scales -- 3.5.3. Comparison of the damage when the S-N curves are linear in either log-log or log-lin scales -- 3.6. Fatigue damage generated by a swept sine vibration on a single-degree-of-freedom linear system -- 3.6.1. General case -- 3.6.2. Linear sweep -- 3.6.3. Logarithmic sweep -- 3.6.4. Hyperbolic sweep -- 3.6.5. General expressions for fatigue damage -- 3.7. Reduction of test time -- 3.7.1. Fatigue damage equivalence in the case of a linear system -- 3.7.2. Method based on fatigue damage equivalence according to Basquin's relationship -- 3.8. Notes on the design assumptions of the ERS and FDS -- Chapter 4. Fatigue Damage Spectrum of a Random Vibration -- 4.1. Fatigue damage spectrum from the signal as function of time -- 4.2. Fatigue damage spectrum derived from a power spectral density -- 4.3. Simplified hypothesis of Rayleigh's law -- 4.4. Calculation of the fatigue damage spectrum with Dirlik's probability density -- 4.5. Up-crossing risk fatigue damage spectrum.

4.6. Reduction of test time -- 4.6.1. Fatigue damage equivalence in the case of a linear system -- 4.6.2. Method based on a fatigue damage equivalence according to Basquin's relationship taking account of variation of natural damping as a function of stress level -- 4.7. Truncation of the peaks of the "input" acceleration signal -- 4.7.1. Fatigue damage spectra calculated from a signal as a function of time -- 4.7.2. Fatigue damage spectra calculated from power spectral densities -- 4.7.3. Comparison of fatigue damage spectra calculated from signals as a function of time and power spectral densities -- 4.8. Sinusoidal vibration superimposed on a broadband random vibration -- 4.8.1. Case of a single sinusoidal vibration superimposed on broadband random vibration -- 4.8.2. Case of several sinusoidal vibrations superimposed on a broadband random vibration -- 4.9. Swept sine superimposed on a broadband random vibration -- 4.9.1. Case of one swept sine superimposed on a broadband random vibration -- 4.9.2. Case of several swept sines superimposed on a broadband random vibration -- 4.10. Swept narrowbands on a broadband random vibration -- Chapter 5. Fatigue Damage Spectrum of a Shock -- 5.1. General relationship of fatigue damage -- 5.2. Use of shock response spectrum in the impulse zone -- 5.3. Damage created by simple shocks in static zone of the response spectrum -- Chapter 6. Influence of Calculation Conditions of ERSs and FDSs -- 6.1. Variation of the ERS with amplitude and vibration duration -- 6.2. Variation of the FDS with amplitude and duration of vibration -- 6.3. Should ERSs and FDSs be drawn with a linear or logarithmic frequency step? -- 6.4. With how many points must ERSs and FDSs be calculated? -- 6.5. Difference between ERSs and FDSs calculated from a vibratory signal according to time and from its PSD.

6.6. Influence of the number of PSD calculation points on ERS and FDS -- 6.7. Influence of the PSD statistical error on ERS and FDS -- 6.8. Influence of the sampling frequency during ERS and FDS calculation from a signal based on time -- 6.9. Influence of the peak counting method -- 6.10. Influence of a non-zero mean stress on FDS -- Chapter 7. Tests and Standards -- 7.1. Definitions -- 7.1.1. Standard -- 7.1.2. Specification -- 7.2. Types of tests -- 7.2.1. Characterization test -- 7.2.2. Identification test -- 7.2.3. Evaluation test -- 7.2.4. Final adjustment/development test -- 7.2.5. Prototype test -- 7.2.6. Pre-qualification (or evaluation) test -- 7.2.7. Qualification -- 7.2.8. Qualification test -- 7.2.9. Certification -- 7.2.10. Certification test -- 7.2.11. Stress screening test -- 7.2.12. Acceptance or reception -- 7.2.13. Reception test -- 7.2.14. Qualification/acceptance test -- 7.2.15. Series test -- 7.2.16. Sampling test -- 7.2.17. Reliability test -- 7.3. What can be expected from a test specification? -- 7.4. Specification types -- 7.4.1. Specification requiring in situ testing -- 7.4.2. Specifications derived from standards -- 7.4.3. Current trend -- 7.4.4. Specifications based on real environment data -- 7.5. Standards specifying test tailoring -- 7.5.1. The MIL-STD -- 7.5.2. The GAM EG 13 standard -- 7.5.3. STANAG 4370 -- 7.5.4. The AFNOR X50-410 standard -- Chapter 8. Uncertainty Factor -- 8.1. Need - definitions -- 8.2. Sources of uncertainty -- 8.3. Statistical aspect of the real environment and of material strength -- 8.3.1. Real environment -- 8.3.2. Material strength -- 8.4. Statistical uncertainty factor -- 8.4.1. Definitions -- 8.4.2. Calculation of uncertainty factor -- 8.4.3. Calculation of an uncertainty factor when the real environment is only characterized by a single value -- Chapter 9. Aging Factor.

9.1. Purpose of the aging factor -- 9.2. Aging functions used in reliability -- 9.3. Method for calculating the aging factor -- 9.4. Influence of the aging law's standard deviation -- 9.5. Influence of the aging law mean -- Chapter 10. Test Factor -- 10.1. Philosophy -- 10.2. Normal distributions -- 10.2.1. Calculation of test factor from the estimation of the confidence interval of the mean -- 10.2.2. Calculation of test factor from the estimation of the probability density of the mean strength with a sample of size n -- 10.3. Log-normal distributions -- 10.3.1. Calculation of test factor from the estimation of the confidence interval of the average -- 10.3.2. Calculation of test factor from the estimation of the probability density of the mean of the strength with a sample of size n -- 10.4. Weibull distributions -- 10.5. Choice of confidence level -- Chapter 11. Specification Development -- 11.1. Test tailoring -- 11.2. Step 1: analysis of the life-cycle profile. Review of the situations -- 11.3. Step 2: determination of the real environmental data associated with each situation -- 11.4. Step 3: determination of the environment to be simulated -- 11.4.1. Need -- 11.4.2. Synthesis methods -- 11.4.3. The need for a reliable method -- 11.4.4. Synthesis method using PSD envelope -- 11.4.5. Equivalence method of extreme response and fatigue damage -- 11.4.6. Synthesis of the real environment associated with an event (or sub-situation) -- 11.4.7. Synthesis of a situation -- 11.4.8. Synthesis of all life profile situations -- 11.4.9. Search for a random vibration of equal severity -- 11.4.10. Validation of duration reduction -- 11.5. Step 4: establishment of the test program -- 11.5.1. Application of a test factor -- 11.5.2. Choice of the test chronology -- 11.6. Applying this method to the example of the "round robin" comparative study.

11.7. Taking environment into account in project management.