Abstract
A model to predict the dynamic response of space flight cables is developed. Despite the influence of cable harnesses on space structures’ dynamics, a predictive model for quantifying the damping effects is not available. To further this research, hysteretic and proportional viscous damping were incorporated in Euler-Bernoulli and Timoshenko beam models to predict the dynamic response of a typical space flight cable, using hysteretic dissipation functions to characterize the damping mechanism. The Euler-Bernoulli beam model was used to investigate the hysteresis functions specifically, and it was determined that including hysteretic dissipation functions in the equations of motion was not sufficient to model the additional modes arising in damped cables; additional damping coordinates in the method of Golla, Hughes and McTavish will be necessary to predict damping behavior when using dissipation functions for this case. A Timoshenko model that included viscous and time hysteresis damping was developed as well, and will ultimately be more appropriate for cable modeling due to the inclusion of shear and rotary inertia terms and damping coefficients.
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Abbreviations
- \( \alpha,\ \beta, {a_i},\ {b_i}\gamma, \delta \) :
-
Dissipation function/history kernel constants
- \( \eta \) :
-
State space vector of displacement solution and derivatives for distributed transfer function method
- \( \rho \) :
-
Density
- \( \psi \) :
-
Total beam rotation
- \( \tau =\sqrt{{\frac{{\rho A{L^4}}}{EI }}} \) :
-
Time parameter
- A :
-
Cross-sectional area
- A d , B d , D d :
-
Dimensionless damping parameters defined within
- C :
-
Dimensionless hysteretic damping parameter containing dissipation function
- c a :
-
Shear damping coefficient
- c b :
-
Rotational damping coefficient
- E :
-
Elastic modulus
- F:
-
Transfer function matrix for use in distributed transfer function method
- G :
-
Shear modulus
- G(s):
-
Dissipation function (transformed into Laplace domain)
- I :
-
Moment area of inertia
- K :
-
Shear coefficient
- L :
-
Beam length
- M, N :
-
Left and right boundary condition matrices for distributed transfer function method
- P 1 , P 2 :
-
Dimensionless beam parameters for bending and rotation, respectively, defined within
- s :
-
Laplace transformed time coordinate
- t :
-
Time coordinate
- T :
-
Axial tension in cable
- T s :
-
Dimensionless tension parameter
- w :
-
Beam displacement as a function of time and distance
- x :
-
Spatial coordinate; distance along the beam in the axial direction
References
Costello GA (1997) Theory of wire rope, 2nd edn. Springer, New York
Jolicoeur C, Cardou A (1996) Semicontinuous mathematical model for bending of multilayered wire strands. J Eng Mech 122(7):643–650
Spak K, Inman D (2012) Model development for cable-harnessed beams. In: 2012 Virginia space grant consortium student research conference, Williamsburg, April 2012
Banks HT, Fabiano RH, Wang Y, Inman DJ, Cudney H (1988) Spatial versus time hysteresis in damping mechanisms. In: Proceedings of the 27th conference on decision and control, Austin, December 1988, pp 1674–1677
Goodding JC, Griffee JC, Ardelean EV (2008) Parameter estimation and structural dynamic modeling of electrical cable harnesses on precision structures. In: 49th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Schaumberg, Illinois, April 2008
Banks HT, Inman DJ (1991) On damping mechanisms in beams. J Appl Mech 58:716–723
Golla DF, Hughes PC (1985) Dynamics of viscoelastic structures—a time-domain, finite element formulation. J Appl Mech 52:897–906
Inman DJ (1989) Vibration analysis of viscoelastic beams by separation of variables and modal analysis. Mech Res Commun 16(4):213–218
Adhikari S (2000) Damping models for structural vibration. Thesis. Cambridge University
Yang B, Tan CA (1992) Transfer functions of one-dimensional distributed parameter systems. J Appl Mech 59:1009–1014
Papailiou KO (1997) On the bending stiffness of transmission line conductors. IEEE Trans Power Del 12(4):1576–1588
Sciulli D (1997) Dynamics and control for vibration isolation design. Thesis. Virginia Tech
Acknowldegements
This work was supported by a NASA Office of the Chief Technologist’s Space Technology Research Fellowship. The first author thanks NASA for generous support and the Virginia Space Grant Consortium for additional funding. The third author gratefully acknowledges the support of AFOSR Grant number FA9550-10-1-0427 monitored by Dr. David Stargel. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.
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© 2013 The Society for Experimental Mechanics, Inc.
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Spak, K., Agnes, G., Inman, D. (2013). Comparison of Damping Models for Space Flight Cables. In: Catbas, F., Pakzad, S., Racic, V., Pavic, A., Reynolds, P. (eds) Topics in Dynamics of Civil Structures, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6555-3_21
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DOI: https://doi.org/10.1007/978-1-4614-6555-3_21
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