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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Frequency (Hz)

dB (

V)

Cable 1, Tension 5 (0 lbs) Response at Point 1-5

Pt 1

2

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510

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2-40

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Frequency (Hz)

dB (

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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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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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20dB

(V

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Freq (Hz)

Compare Cables at Point 4, Three Tie Downs

No CableCable 1

Cable 2

Cable 3

Cable 5Rod

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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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20dB

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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

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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

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