virginia space grant consortium kaitlin spak advisor: dr. daniel inman virginia polytechnic...
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MODELING CABLE EFFECTS ON SPACE
STRUCTURES
Virginia Space Grant Consortium
Kaitlin Spak
Advisor: Dr. Daniel Inman
Virginia Polytechnic Institute and State University
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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:
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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.
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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
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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
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Cable Experiments
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0
10
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Frequency (Hz)
dB (
V)
Cable 1, Tension 5 (0 lbs) Response at Point 1-5
Pt 1
2
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510
110
2-40
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0
10
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30
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Frequency (Hz)
dB (
V)
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.
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.
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Comparison of all cables
at 5 lbs tension.
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102
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0
10
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30
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Frequency (Hz)
dB (
V)
Comparison of Cables for 5lb Tension at Point 2
Cable 1
Cable 2
Cable 3Cable 4
Cable 5
Cabled-Beam Experiments
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101
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-100
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0
20dB
(V
)
Freq (Hz)
Compare Cables at Point 4, Three Tie Downs
No CableCable 1
Cable 2
Cable 3
Cable 5Rod
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0
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dB (
V)
Freq (Hz)
Compare Cables at Point 4, Three Tie Downs
No CableCable 1
Cable 2
Cable 3
Cable 5Rod
Effect of different cables
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0
20dB
(V
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freq (Hz)
Compare cable 2 at all different tie down values at point pnt 4
Bare Beam
T3
T5T7
T9
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Effect of increasing tie downs / decreasing tie down spacing
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.
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101
102
103
-100
-80
-60
-40
-20
0
20dB
(V
)
Freq (Hz)
Compare Cables at Point 4, Three Tie Downs
No CableCable 1
Cable 2
Cable 3
Cable 5Rod
Low frequency noise
With boundary conditions of
At x = 0 and at x = L.
Equations of MotionBased on the application of Hamilton’s principle, the equations of motion for the cabled-beam system are coupled:
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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
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System of interest:
(Length “L” with spring located at “L/2”)
Squared frequencies given by:
Using trial functions for a free-free beam:
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)
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End conditions for free-free beam:
F(s) =
Squared frequencies given by solving the equation:
Natural Frequency ResultsFrequency # Rayleigh- Ritz DTFM Cable 1
1 2.369 TBD 2.188
2 6.74 TBD 4.688
3 13.07 TBD 6.563
4 16.85 TBD 13.13
5 28.0 TBD 27.81
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All values in Hertzk = 10,000 N/m3 springs/tie downs
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
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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
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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