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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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References

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Figures

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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

Tables

Errata

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