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Research Papers

Multimode Dynamics and Out-of-Plane Drift in Suspended Cable Using the Kinematically Condensed Model

[+] Author and Article Information
Lianhua Wang1

College of Civil Engineering, Hunan University, Changsha, Hunan 410082, P.R. China; Key Laboratory of Building Safety and Energy Efficiency, Ministry of Education, 410082, P.R. Chinalhwang@hnu.cn

Yueyu Zhao

College of Civil Engineering, Hunan University, Changsha, Hunan 410082, P.R. Chinayyzhao@hnu.cn

Giuseppe Rega

Department of Structural and Geotechnical Engineering, University of Rome 'La Sapienza', via A. Gramsci 53, Rome 00197, Italygiuseppe.rega@uniroma1.it

1

Corresponding author.

J. Vib. Acoust 131(6), 061008 (Nov 18, 2009) (9 pages) doi:10.1115/1.4000470 History: Received September 09, 2008; Revised July 12, 2009; Published November 18, 2009; Online November 18, 2009

The large amplitude vibration and modal interactions of shallow suspended cable with three-to-three-to-one internal resonances are investigated. The quasistatic assumption and direct approach are used to obtain the condensed suspended cable model and the corresponding modulation equations for the case of primary resonance of the third symmetric in-plane or out-of-plane mode. The equilibrium, periodic, and chaotic solutions of the modulation equations are studied. Moreover, the nonplanar motion and symmetric character of out-of-plane vibration of the shallow suspended cables are investigated by means of numerical simulations. Finally, the role played by the quasistatic assumption, internal resonance, and static configuration in disrupting the symmetry of the out-of-plane vibration is discussed.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

The configurations of cables

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Figure 2

Frequency-response curves of the suspended cable with f3=0.005 when Ω≈ω3in

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Figure 3

(a)Periodic solution branch of the modulation equations when σ3∊(0.015,1.214), (b) eigenvalues of Jacobian when σ3≈0.015, (c) eigenvalues of Jacobian when σ3≈1.214, and (d) Floquet multipliers when σ3≈0.075

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Figure 4

Frequency-response curves of the suspended cable with f3=0.0095 when Ω≈ω3in

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Figure 5

Force-response curves of the suspended cable with σ3=2.5 when Ω≈ω3in

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Figure 6

Frequency-response curves of the suspended cable with p3=0.005 when Ω≈ω3out

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Figure 7

(a) Eigenvalues of Jacobian and (b) periodic solution branch of the modulation equations when σ3≈0.4325

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Figure 8

Frequency-response curves of the suspended cable with p3=0.0095 when Ω≈ω3out

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Figure 9

Force-response curves of the suspended cable with σ3=−5 when Ω≈ω3out

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Figure 10

Dynamic configuration: (a) Ω≈ω3in, σ3=−5.0 and (b) Ω≈ω3out, σ3=−2.5

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Figure 11

Section trajectory: (a) Ω≈ω3in, σ3=−5.0 and (b) Ω≈ω3out, σ3=−2.5

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