Abstract
In the realm of lightweight space structures, the interplay between power and control signal transmission cables and their host structures introduces intriguing dynamics. The presented article aims to investigate optimal geometries for cable placement on plate structures while preserving the dynamic characteristics of the host structure. The cable wrapping is assumed to be periodic such that the cable-harnessed structure consists of several repeating fundamental elements. The periodicity condition allows for the application of an energy-equivalence homogenization approach to develop an analytical model resulting in partial differential equations for the vibrations of the cable-harnessed plate system. An optimization strategy is developed to rank various cable patterns for several host plate structures to obtain the best match for their frequency response functions compared to the bare plate when no cables are attached. Subsequently, a detailed analysis to investigate the impacts of several wrapping parameters on the system’s dynamics is carried out. Lastly, the frequency response functions for the optimal pattern from the analytical solution are validated against those from the finite element model and have shown to be in excellent agreement.
References
1.
Robertson
, L. M.
, Lane
, S. A.
, Ingram
, B. R.
, Hansen
, E. J.
, Babuška
, V.
, Goodding
, J.
, Mimovich
, M.
, Mehle
, G.
, Coombs
, D.
, and Ardelean
, E. V.
, 2007
, “Cable Effects on the Dynamics of Large Precision Structures
,” 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
, Honolulu, HI
, Apr. 23–26
, p. 2389
.2.
Babuška
, V.
, Coombs
, D. M.
, Goodding
, J. C.
, Ardelean
, E. V.
, Robertson
, L. M.
, and Lane
, S. A.
, 2010
, “Modeling and Experimental Validation of Space Structures With Wiring Harnesses
,” J. Spacecr. Rockets
, 47
(6
), pp. 1038
–1052
. .3.
Ardelean
, E. V.
, Goodding
, J. C.
, Mehle
, G.
, Coombs
, D. M.
, Babuška
, V.
, Robertson
, L. M.
, Lane
, S. A.
, Ingram
, B. R.
, and Hansen
, E. J.
, 2007
, “Dynamics of Cable Harnesses on Large Precision Structures
,” 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
, Honolulu, HI
, Apr. 23–26
, p. 2388
.4.
Goodding
, J. C.
, Babuška
, V.
, Griffith
, D. T.
, Ingram
, B. R.
, and Robertson
, L. M.
, 2007
, “Study of Free-Free Beam Structural Dynamics Perturbations Due to Mounted Cable Harnesses
,” 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
, Honolulu, HI
, Apr. 23–26
, p. 2390
.5.
Goodding
, J. C.
, Ardelean
, E. V.
, Babuška
, V.
, Robertson
, L. M.
, and Lane
, S. A.
, 2011
, “Experimental Techniques and Structural Parameter Estimation Studies of Spacecraft Cables
,” J. Spacecr. Rockets
, 48
(6
), pp. 942
–957
. 6.
Spak
, K.
, Agnes
, G.
, and Inman
, D.
, 2013
, “Cable Modeling and Internal Damping Developments
,” Appl. Mech. Rev.
, 65
(1
), p. 010801
. 7.
Spak
, K.
, Agnes
, G.
, and Inman
, D.
, 2013
, “Comparison of Damping Models for Space Flight Cables,” Topics in Dynamics of Civil Structures
, Vol. 4
, F.
Catbas
, S.
Pakzad
, V.
Racic
, A.
Pavic
, and P.
Reynolds
, eds., Springer
, New York
, pp. 183
–194
, ch. 21.8.
Spak
, K. S.
, Agnes
, G. S.
, and Inman
, D. J.
, 2013
, “Toward Modeling of Cable-Harnessed Structures: Cable Damping Experiments
,” 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
, Boston, MA
, Apr. 8–11
, p. 1889
.9.
Spak
, K.
, Agnes
, G.
, and Inman
, D.
, 2014
, “Parameters for Modeling Stranded Cables as Structural Beams
,” Exp. Mech.
, 54
(9
), pp. 1613
–1626
. 10.
Spak
, K. S.
, Agnes
, G. S.
, and Inman
, D. J.
, 2015
, “Modeling Vibration Response and Damping of Cables and Cabled Structures
,” J. Sound Vib.
, 336
, pp. 240
–256
. 11.
Lesieutre
, G. A.
, 2010
, “Frequency-Independent Modal Damping for Flexural Structures Via a Viscous “Geometric” Damping Model
,” J. Guid. Control Dynam.
, 33
(6
), pp. 1931
–1935
. 12.
Lesieutre
, G. A.
, and Kauffman
, J. L.
, 2013
, ““Geometric” Viscous Damping Model for Nearly Constant Beam Modal Damping
,” AIAA J.
, 51
(7
), pp. 1688
–1694
. 13.
Kauffman
, J. L.
, Lesieutre
, G. A.
, and Babuška
, V.
, 2014
, “Damping Models for Shear Beams With Applications to Spacecraft Wiring Harnesses
,” J. Spacecr. Rockets
, 51
(1
), pp. 16
–22
. 14.
Kauffman
, J. L.
, and Lesieutre
, G. A.
, 2013
, “Damping Models for Timoshenko Beams With Applications to Spacecraft Wiring Harnesses
,” 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
, Boston, MA
, Apr. 8–11
, p.1890
.15.
McPherson
, B. N.
, Lesieutre
, G. A.
, and Kauffman
, J. L.
, 2018
, “Investigation of Viscous Damping Terms for a Timoshenko Beam
,” 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
, Kissimmee, FL
, Jan. 8–12
, p. 0456
.16.
Choi
, J.
, and Inman
, D. J.
, 2014
, “Spectrally Formulated Modeling of a Cable-Harnessed Structure
,” J. Sound Vib.
, 333
(14
), pp. 3286
–3304
. 17.
Choi
, J.
, and Inman
, D. J.
, 2013
, “Development of Modeling for Cable Harnessed Structures
,” 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
, Boston, MA
, Apr. 8–11
, p. 1888
.18.
Martin
, B.
, and Salehian
, A.
, 2013
, “Cable-Harnessed Space Structures: A Beam-Cable Approach
,” Proceedings of the 24th International Association of Science and Technology for Development International Conference on Modelling and Simulation
, Banff, Alberta, Canada
, July 17–19
, pp. 280
–284
.19.
Martin
, B.
, and Salehian
, A.
, 2013
, “Vibration Analysis of String-Harnessed Beam Structures: A Homogenization Approach
,” 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
, Boston, MA
, Apr. 8–11
, p. 1892
.20.
Martin
, B.
, and Salehian
, A.
, 2013
, “Dynamic Modelling of Cable-Harnessed Beam Structures With Periodic Wrapping Patterns: A Homogenization Approach
,” Int. J. Model. Simul.
, 33
(4
), pp. 185
–202
. 21.
Martin
, B.
, and Salehian
, A.
, 2016
, “Mass and Stiffness Effects of Harnessing Cables on Structural Dynamics: Continuum Modeling
,” AIAA J.
, 54
(9
), pp. 2881
–2904
. 22.
Martin
, B.
, and Salehian
, A.
, 2014
, “Vibration Modelling of String-Harnessed Beam Structures Using Homogenization Techniques
,” ASME 2014 International Mechanical Engineering Congress and Exposition (IMECE)
, Montreal, Quebec, Canada
, Nov. 14–20
, p. 37039
.23.
Martin
, B.
, and Salehian
, A.
, 2016
, “Homogenization Modeling of Periodically Wrapped String-Harnessed Beam Structures: Experimental Validation
,” AIAA J.
, 54
(12
), pp. 3965
–3980
. 24.
Martin
, B.
, and Salehian
, A.
, 2019
, “Continuum Modeling of Nonperiodic String-Harnessed Structures: Perturbation Theory and Experiments
,” AIAA J.
, 57
(4
), pp. 1736
–1751
. 25.
Martin
, B.
, and Salehian
, A.
, 2018
, “Reference Value Selection in a Perturbation Theory Applied to Nonuniform Beams
,” Shock Vib.
, 2018
. 26.
Martin
, B.
, and Salehian
, A.
, 2020
, “Techniques for Approximating a Spatially Varying Euler-Bernoulli Model With a Constant Coefficient Model
,” Appl. Math. Model.
, 79
, pp. 260
–283
. 27.
Agrawal
, P.
, and Salehian
, A.
, 2021
, “Damping Mechanisms in Cable-Harnessed Structures for Space Applications: Analytical Modeling
,” ASME J. Vib. Acoust.
, 143
(2
), p. 021001
. 28.
Agrawal
, P.
, and Salehian
, A.
, 2021
, “Damping Mechanisms in Cable-Harnessed Structures for Space Applications: Experimental Validation
,” ASME J. Vib. Acoust.
, 143
(2
), p. 024502
. 29.
Yerrapragada
, K.
, and Salehian
, A.
, 2017
, “Coupled Axial, in Plane and Out of Plane Bending Vibrations of Cable Harnessed Space Structures
,” International Conference on Applied Mathematics, Modeling and Computational Science
, Waterloo, Ontario, Canada
, Aug. 20–25
, pp. 249
–257
.30.
Yerrapragada
, K.
, and Salehian
, A.
, 2019
, “Analytical Study of Coupling Effects for Vibrations of Cable-Harnessed Beam Structures
,” ASME J. Vib. Acoust.
, 141
(3
), p. 031001
. 31.
Yerrapragada
, K.
, and Salehian
, A.
, 2018
, “Coupled Bending, Torsion and Axial Vibrations of a Cable-Harnessed Beam With Periodic Wrapping Pattern
,” ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE)
, Quebec City, Quebec, Canada
, Aug. 26–29
, p. 86078
.32.
Yerrapragada
, K.
, and Salehian
, A.
, 2019
, “Coupled Dynamics of Cable-Harnessed Structures: Experimental Validation
,” ASME J. Vib. Acoust.
, 141
(6
), p. 061001
. 33.
Yerrapragada
, K.
, Agrawal
, P.
, and Salehian
, A.
, 2022
, “Multidimensional Vibrations of Cable-Harnessed Beam Structures With Periodic Pattern: Modeling and Experiment
,” Shock Vib.
, 2022
. 34.
Yerrapragada
, K.
, Martin
, B.
, Agrawal
, P.
, and Salehian
, A.
, 2022
, “Fully Coupled Vibrations of Cable-Harnessed Beams With a Non-Periodic Wrapping Pattern
,” Vibration
, 5
(2
), pp. 238
–263
. 35.
Cao
, S.
, Agrawal
, P.
, Qi
, N.
, and Salehian
, A.
, 2021
, “Optimal Geometry for Cable Wrapping to Minimize Dynamic Impacts on Cable-Harnessed Beam Structures
,” ASME J. Vib. Acoust.
, 143
(4
), p. 041005
. 36.
Agrawal
, P.
, and Salehian
, A.
, 2019
, “Vibration Analysis of Cable-Harnessed Plate Structures
,” Proceedings of the 26th International Congress on Sound and Vibration (ICSV26)
, Montreal, Quebec, Canada
, July 7–11
, pp. 2671
–2678
.37.
Agrawal
, P.
, and Salehian
, A.
, 2021
, “Continuum Modeling and Vibration Analysis of Cable-Harnessed Plate Structures of Periodic Patterns
,” ASME J. Vib. Acoust.
, 143
(6
), p. 061007
. 38.
Agrawal
, P.
, and Salehian
, A.
, 2021
, “Vibrations Analysis of Cable-Harnessed Plates: Continuum Modeling and Experimental Validation
,” ASME J. Vib. Acoust.
, 143
(5
), p. 051004
. 39.
Agrawal
, P.
, and Salehian
, A.
, 2022
, “Dynamic Analysis and Experimental Validation of Periodically Wrapped Cable-Harnessed Plate Structures
,” Exp. Mech.
, 62
(6
), pp. 909
–927
. 40.
Coombs
, D. M.
, Goodding
, J. C.
, Babuška
, V.
, Ardelean
, E. V.
, Robertson
, L. M.
, and Lane
, S. A.
, 2011
, “Dynamic Modeling and Experimental Validation of a Cable-Loaded Panel
,” J. Spacecr. Rockets
, 48
(6
), pp. 958
–973
. 41.
Remedia
, M.
, Aglietti
, G. S.
, and Richardson
, G.
, 2015
, “Modelling the Effect of Electrical Harness on Microvibration Response of Structures
,” Acta Astronaut.
, 109
, pp. 88
–102
. 42.
Reddy
, J. N.
, 2006
, Theory and Analysis of Elastic Plates and Shells
, 2nd ed., CRC Press
, Boca Raton, FL
.43.
Meirovitch
, L.
, 1975
, Elements of Vibration Analysis
, McGraw-Hill, Inc
, New York
.44.
Young
, D.
, 1950
, “Vibration of Rectangular Plates by the Ritz Method
,” J. Appl. Mech.
, 17
(4
), pp. 448
–453
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