Research Papers

Analytical Study of Coupling Effects for Vibrations of Cable-Harnessed Beam Structures

[+] Author and Article Information
Karthik Yerrapragada

Department of Mechanical and
Mechatronics Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: kyerrapr@uwaterloo.ca

Armaghan Salehian

Department of Mechanical and
Mechatronics Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: salehian@uwaterloo.ca

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 3, 2018; final manuscript received October 31, 2018; published online January 22, 2019. Assoc. Editor: Matthew Brake.

J. Vib. Acoust 141(3), 031001 (Jan 22, 2019) (15 pages) Paper No: VIB-18-1239; doi: 10.1115/1.4042042 History: Received June 03, 2018; Revised October 31, 2018

This paper presents a distributed parameter model to study the effects of the harnessing cables on the dynamics of a host structure motivated by space structures applications. The structure is modeled using both Euler–Bernoulli and Timoshenko beam theories (TBT). The presented model studies the effects of coupling between various coordinates of vibrations due to the addition of the cable. The effects of the cable's offset position, pretension, and radius are studied on the natural frequencies of the system. Strain and kinetic energy expressions using linear displacement field assumptions and Green–Lagrange strain tensor are developed. The governing coupled partial differential equations for the cable-harnessed beam that includes the effects of the cable pretension are found using Hamilton's principle. The natural frequencies from the coupled Euler, Bernoulli, Timoshenko and decoupled analytical models are found and compared to the results of the finite element analysis (FEA).

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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. 958–974. [CrossRef]
Babuska, 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. [CrossRef]
Goodding, J. , Babuska, V. , Griffith, D. T. , Ingram, B. , and Robertson, L. , 2007, “Studies of Free-Free Beam Structural Dynamics Perturbations Due to Mounted Cable Harnesses,” AIAA Paper No. 2007-2390.
McClure, G. , and Lapointe, M. , 2003, “Modeling the Structural Dynamic Response of Overhead Transmission Lines,” Comput. Struct., 81(8–11), pp. 825–834. [CrossRef]
Spak, K. , Agnes, G. , and Inman, D. , 2014, “Parameters for Modeling Stranded Cables as Structural Beams,” Exp. Mech., 54(9), pp. 1613–1626. [CrossRef]
Witz, J. A. , and Tan, Z. , 1992, “On the Axial-Torsional Structural Behaviour of Flexible Pipes, Umbilicals and Marine Cables,” Mar. Struct., 5(2–3), pp. 205–227. [CrossRef]
Huang, S. , 1999, “Stability Analysis of the Heave Motion of Marine Cable-Body Systems,” Ocean Eng., 26(6), pp. 531–546. [CrossRef]
Robertson, L. , Lane, S. , Ingram, B. , Hansen, E. , Babuska, V. , Goodding, J. , Mimovich, M. , Mehle, G. , Coombs, D. , and Ardelean, E. , 2007, “Cable Effects on the Dynamics of Large Precision Structures,” AIAA Paper No. 2007-2389.
Goodding, J. C. , Ardelean, E. V. , Babuska, 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. [CrossRef]
Ardelean, E. , Goodding, J. , Coombs, D. , Griffee, J. , Babuška, V. , Robertson, L. , and Lane, S. , 2010, “Cable Effects Study: Tangents, Rat Holes, Dead Ends, and Valuable Results,” AIAA Paper No. 2010-2806.
Spak, K. , Agnes, G. , and Inman, D. , 2014, “Cable Parameters for Homogenous Cable-Beam Models for Space Structures,” 32nd IMAC, A Conference and Exposition on Structural Dynamics, Orlando, FL, Feb. 3–6.
Spak, K. S. , Agnes, G. S. , and Inman, D. J. , 2014, “Bakeout Effects on Dynamic Response of Spaceflight Cables,” J. Spacecr. Rockets, 51(5), pp. 1721–1734. [CrossRef]
Spak, K. S. , 2014, “Modeling Cable Harness Effects on Spacecraft Structures,” Ph.D. dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA. https://vtechworks.lib.vt.edu/handle/10919/49302
Spak, K. S. , Agnes, G. S. , and Inman, D. , 2013, “Towards Modeling of Cable-Harnessed Structures: Cable Damping Experiments,” AIAA Paper No. 2013-1889.
Choi, J. , and Inman, D. J. , 2014, “Spectrally Formulated Modeling of a Cable-Harnessed Structure,” J. Sound Vib., 333(14), pp. 3286–3304. [CrossRef]
Huang, Y.-X. , Tian, H. , and Zhao, Y. , 2016, “Effects of Cable on the Dynamics of a Cantilever Beam With Tip Mass,” Shock Vib., 2016, p. 7698729.
Huang, Y.-X. , Tian, H. , and Zhao, Y. , 2017, “Dynamic Analysis of Beam-Cable Coupled Systems Using Chebyshev Spectral Element Method,” Acta Mech. Sin., 33(5), pp. 954–962. [CrossRef]
Martin, B. , and Salehian, A. , 2013, “Cable-Harnessed Space Structures: A Beam-Cable Approach,” 24th International Association of Science and Technology for Development International Conference on Modelling and Simulation, Banff, AB, Canada, July 17–19, pp. 280–284.
Martin, B. , and Salehian, A. , 2013, “Dynamic Modelling of Cable-Harnessed Beam Structures With Periodic Wrapping Patterns: A Homogenization Approach,” Int. J. Modell. Simul., 33(4), pp. 185–202. https://www.tandfonline.com/doi/abs/10.2316/Journal.205.2013.4.205-5981
Martin, B. , and Salehian, A. , 2013, “Vibration Analysis of String-Harnessed Beam Structures: A Homogenization Approach,” AIAA Paper No. 2013-1892.
Martin, B. , and Salehian, A. , 2014, “Vibration Modelling of String-Harnessed Beam Structures Using Homogenization Techniques,” ASME Paper No. IMECE2014-37039.
Martin, B. , and Salehian, A. , 2016, “Homogenization Modeling of Periodically Wrapped String-Harnessed Beam Structures: Experimental Validation,” AIAA J., 54(12), pp. 3965–3980. [CrossRef]
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. [CrossRef]
Salehian, A. , Cliff, E. M. , and Inman, D. J. , 2006, “Continuum Modeling of an Innovative Space-Based Radar Antenna Truss,” J. Aerosp. Eng., 19(4), pp. 227–240. [CrossRef]
Salehian, A. , Inman, D. J. , and Cliff, E. M. , 2006, “Natural Frequency Validation of a Homogenized Model of a Truss,” XXIV-International Modal Analysis Conference, St. Louis, MO, Jan. 30–Feb. 2.
Salehian, A. , Seigler, T. M. , and Inman, D. J. , 2007, “Dynamic Effects of a Radar Panel Mounted on a Truss Satellite,” AIAA J., 45(7), pp. 1642–1654. [CrossRef]
Salehian, A. , and Inman, D. J. , 2008, “Dynamic Analysis of a Lattice Structure by Homogenization: Experimental Validation,” J. Sound Vib., 316(1–5), pp. 180–197. [CrossRef]
Salehian, A. , and Inman, D. J. , 2010, “Micropolar Continuous Modeling and Frequency Response Validation of a Lattice Structure,” ASME J. Vib. Acoust., 132(1), p. 011010. [CrossRef]
Salehian, A. , and Chen, Y. , 2012, “On Strain-Rate Dependence of Kinetic Energy in Homogenization Approach: Theory and Experiment,” AIAA J., 50(10), pp. 2029–2033. [CrossRef]
Stoykov, S. , and Ribeiro, P. , 2013, “Vibration Analysis of Rotating 3D Beams by the P-Version Finite Element Method,” Finite Elem. Anal. Des., 65, pp. 76–88. [CrossRef]
Stoykov, S. , and Margenov, S. , 2014, “Nonlinear Vibrations of 3D Laminated Composite Beams,” Math. Probl. Eng., 2014, p. 892782.
Fonseca, J. R. , and Ribeiro, P. , 2006, “Beam P-Version Finite Element for Geometrically Non-Linear Vibrations in Space,” Comput. Methods Appl. Mech. Eng., 195(9–12), pp. 905–924. [CrossRef]
Stoykov, S. , and Ribeiro, P. , 2010, “Nonlinear Forced Vibrations and Static Deformations of 3D Beams With Rectangular Cross Section: The Influence of Warping, Shear Deformation and Longitudinal Displacements,” Int. J. Mech. Sci., 52(11), pp. 1505–1521. [CrossRef]
Tanaka, M. , and Bercin, A. N. , 1997, “Finite Element Modelling of the Coupled Bending and Torsional Free Vibration of Uniform Beams With an Arbitrary Cross-Section,” Appl. Math. Modell., 21(6), pp. 339–344. [CrossRef]
Song, O. , Ju, J.-S. , and Librescu, L. , 1998, “Dynamic Response of Anisotropic Thin-Walled Beams to Blast and Harmonically Oscillating Loads,” Int. J. Impact Eng., 21(8), pp. 663–682. [CrossRef]
Stephen, N. G. , and Zhang, Y. , 2006, “Coupled Tension–Torsion Vibration of Repetitive Beam-Like Structures,” J. Sound Vib., 293(1–2), pp. 253–265. [CrossRef]
Vörös, G. M. , 2009, “On Coupled Bending–Torsional Vibrations of Beams With Initial Loads,” Mech. Res. Commun., 36(5), pp. 603–611. [CrossRef]


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Fig. 1

Representation of the cable harness beam along with the coordinate axes

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Fig. 2

Vibrations mode shapes for fixed-fixed boundary conditions using coupled EB theory for the first two modes

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Fig. 3

Vibrations mode shapes for cantilever boundary conditions using coupled EB theory for the first two modes

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Fig. 4

Vibrations mode shapes for simply supported boundary conditions using coupled EB theory for the first two modes

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Fig. 5

Percentage for the strain energy contribution of each modal coordinate with respect to mode number

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Fig. 6

Effects of cable radius on the coupled natural frequencies

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Fig. 7

Error comparisons for natural frequencies between the coupled and decoupled models and the FEA

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Fig. 8

Effect of cable offset position on the coupled natural frequencies

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Fig. 9

Strain energy and natural frequency with respect to cable offset position

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Fig. 10

Effect of cable pretension on the natural frequencies for first in-plane bending, out-of-plane bending and torsional mode using the system parameters of Table 5

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Fig. 11

Bar graph of strain energy contributions for mode 1 for beam with parameters from (a) Table 1 (b) Table 5 for fixed-fixed boundary condition

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Fig. 12

Frequency response function for cantilever boundary condition



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