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Technical Brief

Axial–Torsional Vibrational Modes of Braided and Trapezoidal Wires

[+] Author and Article Information
Mohammed K. Alkharisi

Department of Civil and Environmental Engineering,
Colorado State University,
Fort Collins, CO 80523
e-mail: mohammed.alkharisi@colostate.edu

Paul R. Heyliger

Department of Civil and Environmental Engineering,
Colorado State University,
Fort Collins, CO 80523
e-mail: prh@engr.colostate.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 7, 2018; final manuscript received August 29, 2018; published online October 23, 2018. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 141(2), 024501 (Oct 23, 2018) (7 pages) Paper No: VIB-18-1250; doi: 10.1115/1.4041398 History: Received June 07, 2018; Revised August 29, 2018

The coupled axial–torsional modes of vibration are examined for three common types of braided wires: the well-known (1 + 6) configuration, the trapezoidal configuration, and the so-called twisted-pair. Representative volume elements of these systems with angles of twist ranging from 0 deg to 30 deg are described using three-dimensional elasticity theory and subjected to pure axial deformation and then pure twist to determine the stiffness coefficients that are used to describe the force–displacement relationship. These are compared with the results of existing braided wire models for the (1 + 6) geometry. Both analytical and finite element models of all three wires are then introduced to determine the level of coupling between the axial and torsional modes of vibration for representative homogeneous and composite cables.

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Figures

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Fig. 1

Simple straight (1 + 6) configuration

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Fig. 2

The trapezoidal wire

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Fig. 3

The twisted pair configuration

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Fig. 4

The extensional stiffness Kεε for the (1 + 6) model cable for the present 3D finite element method (FEM) approach and comparative one-dimensional models as a function of lay angle

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Fig. 5

The coupling stiffness Kθε for the (1 + 6) model cable for the present 3D FEM approach and comparative one-dimensional models as a function of lay angle

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Fig. 6

The torsional stiffness Kθθ for the (1 + 6) model cable for the present 3D FEM approach and comparative one-dimensional models as a function of lay angle

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Fig. 7

The axial displacement modal shapes for the lowest frequency of the composite wire for lay angles of 5, 10, 15, 20, 25, and 30 deg. The amplitudes increase with lay angle since they are normalized with respect to twist. The vertical dashed lines indicate intercable boundaries.

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