1. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 1 Shock and Vibration in Launch Vehicles By Tom Irvine

2. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 2 Website www.vibrationdata.com Username: vibration Password: quake

3. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 3 Shock & Vibration Analysis Areas Structural Dynamics Environments

4. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 4 Structural Dynamics  Analyze natural frequencies and mode shapes of the launch vehicle and payload system  Coupled-loads analysis to determine payload stresses and deflections  Verify that the control system algorithm accounts for vehicle body- bending frequency  Verify that the launch vehicle and payload can withstand seismic and wind loading while the vehicle is on the launch pad  Tools: finite element method and modal testing

5. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 5 Pegasus XL 9.0 Hz Bending Mode

6. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 6 Environments Transportation and Shipping Shock Motor Ignition Shock Launch Vibroacoustics Pyrotechnic Shock from Stage Separation Events Aerodynamic Flow Excitation Motor Pressure Oscillation Flight Anomalies The launch vehicle avionics and the payload must be designed and tested to withstand shock and vibration environments.

7. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 7 Environment Flow Chart Derive Environments using Empirical Data Test Components and Payload Write Test Plan Launch the Vehicle Post-flight Data Analysis Check for Anomalies

8. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 8 Environments Analysis Tools Empirical methods are the primary tools for predicting shock and vibration levels Extrapolate levels from test data Static fire test of a rocket motor Stage separation test Wind tunnel test Extrapolate levels from flight data

9. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 9 Typical Specification Formats EnvironmentFormat Sine VibrationSine Sweep Random VibrationPower Spectral Density ShockShock Response Spectrum

10. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 10 MIL-STD-1540D - Product Verification Requirements for Launch, Upper-Stage, and Space Vehicles MIL-HDBK-340A - Test Requirements for Launch, Upper-Stage, and Space Vehicles MIL-STD-810F - Test Standard for Environmental Engineering Considerations and Laboratory Tests NASA CR 116406 - Aerospace System Pyrotechnic Shock Data Laganelli, A.L., Wolfe, H.F., "Prediction of Fluctuating Pressure in Attached and Separated Turbulent Boundary Layer Flow," AIAA Paper AIAA-89-1064, April 1989. V. Alley and S. Leadbetter, Prediction of Natural Vibrations of Multistage Launch Vehicles, AIAA Journal. Environments Analysis References

11. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 11 Environments Analysis References (continued) D. Steinberg, Vibration Analysis for Electronic Equipment, Wiley-Interscience, New York, 1988. and many others

12. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 12 Development Tests Perform development tests to characterize shock and vibration environments

13. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 13 Linear Shape Charge Test Derive shock environment from accelerometer measurements.

14. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 14 Motor Static Fire Test

15. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 15 Flight Vibration Derivation Derive flight vibration environment using empirical techniques. Vibration depends on vehicle geometry, material, Mach number, air density and flow regime.

16. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 16 Aerodynamic Flow Vibration: Attached Flow Cone-Cylinder Geometry, Transonic Shockwave Oscillation with Attached Flow Cone-Cylinder Geometry, Supersonic, Attached Flow

17. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 17 Aerodynamic Flow Vibration: Compression Corner Cone-Cylinder Geometry with Separated Flow near Compression Corner, Transonic Cone-Cylinder Geometry with Separated Flow near Compression Corner and Shockwaves, Supersonic

18. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 18 Aerodynamic Flow Vibration: Boat-tail Shockwave Oscillation with Boat- tail Induced Separation, Transonic Attached Flow with Boat-tail Induced Separation and Shockwave Oscillation, Supersonic

19. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 19 L1011 & Pegasus Aerodynamic flow interaction between L1011 and Pegasus

20. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 20 Testing Avionics components and payload must be tested to the resulting shock and vibration environments. Components include Flight Computer Inertial Navigation System (INS) Telemetry Transmitter C-Band Transponder Antennas Battery Boxes Flight Termination System

21. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 21 Shaker Table Test Apply base excitation to the test item. Verify that the item can withstand the vibration environment. The test item should be powered and monitored during the vibration test.

22. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 22 Flight Accelerometer Data

23. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 23

24. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 24 Time-Domain Curve-Fitting Demonstrate a time-domain, curve-fitting method for analyzing accelerometer data. The method is innovative in that it uses random number generation to determine the characteristics of the measured data. These characteristics include the amplitude, frequency, phase angle, and damping ratio of the signal's components.

25. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 25 Variables y(t) Amplitude Function A Amplitude constant nn Natural frequency  Damping ratio  Phase angle t Time

26. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 26 Candidate Functions for Data Curve-fit Pure Sine Series of Pure Sinusoids Lightly-damped Sine

27. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 27 Pegasus

28. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 28 Example 1: Pegasus Drop Transient Consider the Pegasus  launch vehicle mounted underneath an L-1011. The most significant event for the payload is the drop transient from the carrier aircraft. The Pegasus vehicle is like a free-free beam subjected to an initial displacement that varies along its length. During the five-second free-fall interval, the initial strain energy is released, causing the Pegasus vehicle to experience a damped, transient oscillation.

29. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 29 Example 1: Damped Sine Data

30. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 30 Pegasus User’s Guide To minimize coupling of the payload bending modes with the launch vehicle first bending mode, the first fundamental lateral frequency must be greater than 20 Hz, cantilevered from the base of the spacecraft, excluding the spacecraft separation system. (octave rule)

31. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 31 Example 1: Numerical Results AmplitudeA0.92 Natural Frequency fn9.56 Hz Damping  1.2% Phase  6.108 rad

32. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 32 Example 2: M57A1 Motor Resonance The M57A1 motor is a solid-fuel motor originally developed as a third stage for the Minuteman missile program. This motor has since been used on a variety of suborbital vehicles, such as target vehicles. The M57A1 has a distinct pressure oscillation. The oscillation frequency sweeps downward from 530 Hz to 450 Hz over a 16-second duration.

33. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 33 Minuteman II Stage III (M57A1)

34. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 34 Example 2: Frequency Variation

35. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 35 Example 2: Time History

36. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 36 Example 2: Numerical Results AmplitudeA0.82 G Oscillation Frequency fn488.2 Hz Phase  1.048 rad

37. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 37 Example 3. Flight Anomaly – TVC System

38. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 38 Example 3: Segment

39. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 39 Example 3: Numerical Results ParameterDominant Signal Harmonic Amplitude1.5 G0.71 G Oscillation Frequency12.5 Hz37.4 Hz Phase0.854 rad3.672 rad The data reveals the dominant forcing frequency and a 3X harmonic. This data could be used to troubleshoot the anomaly.

40. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 40 Example 4: Launch Vehicle Transportation A suborbital launch vehicle is being integrated at a missile assembly building (MAB) at Vandenberg AFB. The distance from the MAB to the launch pad is 20 miles. The assembled launch vehicle will be mounted horizontally on a custom trailer for transportation from the MAB to the pad. The launch vehicle must withstand the lateral loading that occurs as the tractor-trailer crosses over potholes, railroad tracks, and joints at bridges.

41. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 41 Example 4: Time History

42. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 42 Example 4: Synthesis Equation Steps: Synthesize the first damped sinusoid. Subtract it from the signal. Synthesize the next damped sinusoid. Repeat these steps until n sinusoids are synthesized.

43. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 43 Example 4: Numerical Results ComponentAmplitude (G) Frequency (Hz) Phase (rad) DampingDelay (sec) 10.1095.224.9250.5%0.776 20.1095.066.3111.2%0.881 30.0402.535.9790.6%0.078 40.0452.640.9291.3%4.638 50.0121.180.5170.2%1.438 The synthesis consisted of 30 damped sinusoids. Only the top five are shown for brevity. The sinusoids near 5 Hz were due to launch vehicle bending modes. The spectral components near 1 Hz and 2.5 Hz were primarily due to the trailer suspension, with the launch vehicle acting as a rigid-body.

44. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 44 Example 4: Fourier Transform

45. Vibrationdata AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS 45 Conclusion Characterization of shock and vibration environments, as well as structural dynamics, helps ensure mission success.