1. Virginia Space Grant Consortium Kaitlin Spak Advisor: Dr. Daniel Inman Virginia Polytechnic Institute and State University

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3. Deep Impact Spacecraft Cable and wiring wrapped in orange Kapton tape TRENDS: Number of cables on spacecraft: or Spacecraft material mass: Launch cost due to mass reduction: Percentage of mass made up of cables: 3

4. As spacecraft mass decreases due to lightweight material development, cable harnesses and wiring make up a larger percentage of the total mass. Cables were originally included as non-structural lumped mass, but their effects as structural mass can no longer be ignored. Long-Term Project Goal: Develop models to characterize, describe and predict the effects of structural cable mass on the dynamic response of space structures. Short Term Project Goal: Develop models to characterize and describe the effects of structural cable mass on the dynamic response of a simple beam. 4

5.  Year 1: Develop simple models using two different methods, get good experimental data at high and low frequencies, begin validating models and adding complexity to the models as needed  Year 2: Add complexity to models for complete validation, then focus on including damping and more accurate ways to model the flexible cable 5

6. What’s Been Done to Date  Initial reading, investigation of many types of model  Experiments at CIMSS Lab, Virginia Tech  Rayleigh Ritz Method  Distributed Transfer Function Method 6

7. Cable Experiments 7

8. 8 Cable 1, 5 lbs tension. Neat and clean with natural frequencies easily recognizable. Cable 1, 0 lbs tension (slack). Natural frequencies less defined. Each line is the response measured from a different point on the beam.

9. Result: Cables have good frequency response behavior, but cannot be modeled simply as strings or as Euler-Bernoulli beams. Rotary inertia must be included as a minimum, as well as taking cable tension into account. 9 Comparison of all cables at 5 lbs tension.

10. Cabled-Beam Experiments 10

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12. 12 Effect of different cables

13. 13 Effect of increasing tie downs / decreasing tie down spacing

14. Result: Experiments performed at Virginia Tech yielded good results for high frequency ranges, but need to be improved for lower frequencies where models will have high fidelity. Useful for designing the experiment, looking for overall trends, and setting up programs to analyze data. 14 Low frequency noise

15. With boundary conditions of At x = 0 and at x = L. Equations of Motion Based on the application of Hamilton’s principle, the equations of motion for the cabled-beam system are coupled: 15

16. Rayleigh Ritz Modeling  Combines Rayleigh method, which approximates the lowest natural frequency, with the Ritz method, which calculates higher natural frequencies based on energy methods  VERY dependent on an assumed mode shape for a trial function  An approximation at best 16

17. 17 System of interest: (Length “L” with spring located at “L/2”) Squared frequencies given by: Using trial functions for a free-free beam:

18. Distributed Transfer Function Method  Exact solution  Based on the Laplace transform of the equations of motion  Can be used to combine separate systems (such as a beam and a cable)  May be computationally challenging to determine e^F(s) 18

19. 19 End conditions for free-free beam: F(s) = Squared frequencies given by solving the equation:

20. Natural Frequency Results Frequency # Rayleigh- RitzDTFMCable 1 12.369TBD2.188 26.74TBD4.688 313.07TBD6.563 416.85TBD13.13 528.0TBD27.81 20 All values in Hertz k = 10,000 N/m 3 springs/tie downs

21. Future Work  Acquire actual space cables  Perform cable testing with space-worthy cables  Perform cabled-beam testing with space- worthy cables, emphasizing lower- frequency response range  Model cable as Timoshenko beam in RR model  Determine F(s) and finish DTFM model Year One: April 2012 – August 2012 21

22. Future Work  Complete experimental procedures and establish cabled-beam database  Add tie-down damping to RR model  Add internal damping to both models  Increase model complexity to validate models  Complete and defend dissertation Year Two: August 2012 – August 2013 22

23. Acknowledgments  Virginia Space Grant Consortium  National Aeronautics and Space Administration  Jet Propulsion Laboratory  Air Force Office of Scientific Research  Center for Intelligent Material Systems and Structures  Dr. Daniel Inman and Dr. Gregory Agnes