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Research Papers

In-Plane Free Vibrations of an Inclined Taut Cable

[+] Author and Article Information
Xiaodong Zhou

Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, Chinazhou-xd06@mails.tsinghua.edu.cn

Shaoze Yan

Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, Chinayansz@mail.tsinghua.edu.cn

Fulei Chu1

Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, Chinachufl@mail.tsinghua.edu.cn

1

Corresponding author.

J. Vib. Acoust 133(3), 031001 (Mar 24, 2011) (9 pages) doi:10.1115/1.4003397 History: Received February 26, 2010; Revised September 27, 2010; Published March 24, 2011; Online March 24, 2011

The investigation of the free vibrations of inclined taut cables has been a significant subject due to their wide applications in various engineering fields. For this subject, accurate analytical expression for the natural modes and the natural frequencies is of great importance. In this paper, the free vibration of an inclined taut cable is further investigated by accounting for the factor of the weight component parallel to the cable chord. Two coupled linear differential equations describing two-dimensional in-plane motion of the cable are derived based on Newton’s law. By variable substitution, the equation of the transverse motion becomes a Bessel equation of zero order when the equation of longitudinal motion is ignored. Solving the Bessel equation with the given boundary conditions, a set of explicit formulae is presented, which is more accurate for determining the natural frequencies and the modal shapes of an inclined taut cable. The accuracy of the proposed formulae is validated by numerical results obtained by the Galerkin method. The influences of two characteristic parameters λ and ε on the natural frequencies and modal shapes of an inclined taut cable are studied. The results are discussed and compared with those of other literatures. It appears that the present theory has an advantage over others in the aspect of accuracy, and may be used as a base for the correct analysis of linear and nonlinear dynamics of cable structures.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Definition diagram for cable static profile and vibrations: (a) coordinate definition of an inclined cable and (b) equilibrium of a differential cable element

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Figure 2

The first four nondimensional frequency ratios versus λ/π for different values of ε

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Figure 3

The first four nondimensional frequency ratios versus ε for different values of λ/π

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Figure 4

The changing of the first four nondimensional frequency ratios versus parameter λ by Eq. 15

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Figure 5

The changing of the first four nondimensional frequency ratios versus parameter λ by Eq. 17

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Figure 6

The enlarged views of the two veering zones

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Figure 7

The first two longitudinal and transverse modal shapes of an inclined taut cable with an inclination angle of 60 deg

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