Appendix K Mathematical Elements Involved in the Estimation of Uncertainties (Supplementary). 1.1. Problem -- 1.1.1. Justification of tests in a mechanical environment -- 1.1.2. Quality of environmental tests -- 1.1.3. Generating sets of vibrations -- 1.1.4. "Shock and vibration" terminology -- 1.1.5. Testing methods -- 1.1.6. Uncertainty in measurement -- 1.1.7. Interlaboratory comparison and proficiency testing -- 1.1.8. Metrology management -- 1.2. Different types of mechanical signals -- 1.2.1. Overview -- 1.2.2. Mathematical prerequisites -- 1.2.3. Types of mechanical signals -- 1.2.4. The different types of mechanical signals -- a practical approach -- 1.3. Theory of vibration -- reminders -- 1.3.1. Fundamental law of dynamics -- 1.3.2. Concept of DOF -- 1.3.3. Systems comprising 1 DOF -- 1.3.4. Free oscillations of an undamped system -- 1.3.5. Free oscillations from an undamped system -- 1.3.6. Forced oscillations of a damped system -- 1.3.7. Systems with several coupled DOF -- 1.4. Concept of mechanical impedance -- 1.4.1. Overview -- 1.4.2. Definitions -- 1.4.3. Resonance and antiresonance -- 1.4.4. Problems with environmental laboratory simulation -- 1.4.5. Conclusion -- 1.5. Electromechanical analogies -- 1.5.1. Overview -- 1.5.2. Maxwell's analogy of the "force tension" type -- 1.5.3. Darrieus' Analogy "force intensity' -- 1.5.4. Units and electrical mechanical correspondence -- 1.5.5. Establishment of electric diagrams -- 1.6. Analog and logic computer simulation -- 1.6.1. Overview -- 1.6.2. Structure of an analog and logic calculator -- 1.6.3. Resolution of various systems -- 1.6.4. Sequential programming of analog computers -- 1.7. Conclusion -- ch. 2 Signal Analysis -- 2.1. Overview -- 2.1.1. Temporal or spectral form -- 2.1.2. Correlation functions -- 2.1.3. Probabilities -- 2.1.4. Spectral analysis -- 2.1.5. Notion of shock spectrum -- 2.2. Spectral density of power -- 2.2.1. Overview -- 2.2.2. PSD Study -- 2.3. FS-Fourier Integral -- 2.3.1. Overview -- 2.3.2. Considerations of use -- 2.3.3. Analysis of the results -- 2.3.4. Calculation example -- ch. 3 Test Preparation -- 3.1. Test demand analysis and associated test specifications -- 3.1.1. Review of testing demand -- 3.1.2. Test specifications analysis -- 3.1.3. Commercial proposal or contract -- 3.1.4. Order review -- 3.2. Test initiation -- 3.3. Test fixtures -- 3.3.1. Overview -- 3.3.2. Principles of construction -- 3.3.3. Concepts of strenght of materials -- 3.3.4. Manufacturing influence -- 3.3.5. Conclusion -- 3.4. Test execution -- 3.5. Test reporting -- ch. 4 Testing -- 4.1. Sine vibration tests -- 4.1.1. Fixed frequency testing -- 4.1.2. Swept sine tests -- 4.1.3. Conclusion -- 4.2. Vibration testing in noise or random -- 4.2.1. Overview -- 4.2.2. Concepts on random functions -- 4.2.3. Random vibrations -- 4.3. Specific tests -- ch. 5 Equipment Applications -- 5.1. Vibration sources and effects -- 5.1.1. Overview -- 5.1.2. Vibration sources -- 5.1.3. Vibration effects -- 5.1.4. Notions of fatigue and damage due to vibrations -- 5.2. Electronic equipment -- 5.2.1. In land vehicles -- 5.2.2. In ships and submarines -- 5.2.3. In aircrafts, helicopters, missiles -- 5.2.4. Conclusion -- 5.3. Design of electronic equipment subjected to vibrations -- 5.3.1. Operating mode -- 5.3.2. Design techniques -- 5.3.3. Printed circuit boards -- 5.3.4. Components assembly -- 5.3.5. Cases -- 5.3.6. Wiring -- 5.3.7. Conclusion -- 5.4. Study of a particular case -- example of analysis of an electronic bay -- ch. 6 Controlling Generators of Vibrations and Shocks -- 6.1. General principles -- 6.2. Typical configuration of the equipment used -- 6.3. Traceability of tests -- 6.4. Control in sinusoidal mode -- 6.4.1. Generalities -- 6.4.2. Generating a signal -- 6.4.3. Signal acquisition -- 6.4.4. Measurements -- 6.4.5. Corrections -- 6.4.6. Safety devices on controllers -- 6.4.7. Safety devices on the measuring channels -- 6.4.8. Back-ups -- 6.4.9. Deferred time -- 6.5. Random control -- 6.5.1. Signal generation -- 6.5.2. Acquisition of measurements -- 6.6. Shock and transient control -- 6.6.1. Generation in temporal form -- 6.6.2. Generation and control in the shock spectrum -- 6.7. Combined vibrations control -- 6.7.1. Overview -- 6.7.2. Methods -- 6.7.3. Current and emerging needs -- 6.8. Control: a few essential rules -- ch. 7 Metrology of Measurement and Testing Methods -- 7.1. Introduction to accelerometer sensors -- 7.1.1. Overview -- 7.1.2. Principle of operation -- 7.1.3. Main features -- 7.1.4. Calibration of accelerometer sensors -- 7.1.5. Accuracy of accelerometers -- 7.1.6. Sensor installation rules -- 7.2. Measurement amplifiers -- 7.2.1. Overview -- 7.2.2. Equivalent circuit -- 7.2.3. Voltage amplifier -- 7.2.4. Charge converters -- 7.3. Validation and verification of the testing means -- 7.4. Control of metrology in a testing laboratory -- ch. 8 Testing Means for Vibrations -- 8.1. Electrodynamic exciters -- 8.1.1. Brief description of an electrodynamic exciter -- 8.1.2. Impact opportunities and performance -- 8.1.3. Producing an acceleration pulse on the movable table of a shaker -- 8.1.4. Modeling an electrodynamic exciter -- 8.1.5. Evaluation of the modeling parameters -- 8.2. Hydraulic exciters -- 8.2.1. Overview -- 8.2.2. Principle of operation -- 8.2.3. Hydraulic operation equations -- 8.2.4. Use in impact tests -- 8.2.5. Conclusion -- Conclusion -- Appendices -- Appendix A Fundamental Laws of Hydraulics -- Application to the Study of Hydraulic Vibration Generators -- Appendix B Study of the Basic Model with Damping -- Appendix C Natural Frequencies of 1,6 mm Thick Cards Equipped with Stiffeners -- Appendix D Resonance Frequencies of IC Cards Depending on the Mounting Conditions -- Appendix E Concept of Cepstrum -- Appendix F Tolerances on Vibration Fixtures -- Appendix G Determining Measurement Uncertainty -- Example of a Calibration Method for Accelerometer Sensors -- Appendix H Example of MPE Allowances -- Appendix I List of Testing Methods in Standard Environments -- Appendix J Control Strategies -- Simplified Summary -- Appendix K Mathematical Elements Involved in the Estimation of Uncertainties (Supplementary).
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