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Research Papers

Nonlinear Vibrations Analysis of Overhead Power Lines: A Beam With Mass–Spring–Damper–Mass Systems

[+] Author and Article Information
Mohammad A. Bukhari

College of Science and Engineering,
Central Michigan University,
Mt. Pleasant, MI 48859
e-mail: bukha2m@cmich.edu

Oumar R. Barry

College of Science and Engineering,
Central Michigan University,
Mt. Pleasant, MI 48859
e-mail: barry1o@cmich.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 19, 2017; final manuscript received November 14, 2017; published online January 24, 2018. Assoc. Editor: Alper Erturk.

J. Vib. Acoust 140(3), 031004 (Jan 24, 2018) (10 pages) Paper No: VIB-17-1166; doi: 10.1115/1.4038807 History: Received April 19, 2017; Revised November 14, 2017

This paper examines the nonlinear vibration of a single conductor with Stockbridge dampers. The conductor is modeled as a simply supported beam and the Stockbridge damper is reduced to a mass–spring–damper–mass system. The nonlinearity of the system stems from the midplane stretching of the conductor and the cubic equivalent stiffness of the Stockbridge damper. The derived nonlinear equations of motion are solved by the method of multiple scales. Explicit expressions are presented for the nonlinear frequency, solvability conditions, and detuning parameter. The present results are validated via comparisons with those in the literature. Parametric studies are conducted to investigate the effect of variable control parameters on the nonlinear frequency and the frequency response curves. The findings are promising and open a horizon for future opportunities to optimize the design of nonlinear absorbers.

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Figures

Grahic Jump Location
Fig. 2

Schematic of a simply supported beam with an in-span mass-spring-damper-mass systems

Grahic Jump Location
Fig. 1

Schematic of a single conductor with a stockbridge dampers

Grahic Jump Location
Fig. 10

Frequency–response curves for variables values oftension: ξ1=0.1,ξ2=0.9,α11=α12=0.01,α21=α22=0.5,kp=2π4,γp=kp/6,f=5,μ=0.2

Grahic Jump Location
Fig. 4

Nonlinear frequency versus vibration amplitude for different dampers location: s=2,α11=α12=0.01,α21=α22=0.1,kp=2π4,γp=kp/6

Grahic Jump Location
Fig. 5

Nonlinear frequency versus vibration amplitude for different in-span mass values: s=2,ξ1=0.1,ξ2=0.9,α21=α22=0.1,kp=2π4,γp=kp/6

Grahic Jump Location
Fig. 6

Nonlinear frequency versus vibration amplitude for different suspended mass values: s=2,ξ1=0.1,ξ2=0.9,α11=α12=0.01,kp=2π4,γp=kp/6

Grahic Jump Location
Fig. 7

Detuning from the linear natural frequency versus vibration amplitude for different values of tension: ξ1=0.1,ξ2=0.9,α11=α12=0.01,α21=α22=0.1,kp=2π4,γp=kp/6

Grahic Jump Location
Fig. 8

Detuning from the linear natural frequency versus vibration amplitude for different values of spring stiffness: s=2,ξ1=0.1,ξ2=0.9,α11=α12=0.01,α21=α22=0.1,γp=kp/6

Grahic Jump Location
Fig. 9

Detuning from the linear natural frequency versus vibration amplitude for different values of spring stiffness: s=2,ξ1=0.1,ξ2=0.9,α11=α12=0.01,α21=α22=0.5,γp=kp/6

Grahic Jump Location
Fig. 3

Validating the current results: s = 0, α11 = α12 = 0.5, α21 = α22 = 0, kp = γp = 2π4, μ = 0.2, v = 0

Grahic Jump Location
Fig. 11

Frequency–response curves for different values of in-span mass: s=2,ξ1=0.1,ξ2=0.9,α21=α22=0.1,kp=2π4,γp=kp/6,f=5,μ=0.2

Grahic Jump Location
Fig. 12

Frequency–response curves for different values of suspended mass: s=2,ξ1=0.1,ξ2=0.9,α11=α12=0.01,kp=2π4,γp=kp/6,f=5,μ=0.2

Grahic Jump Location
Fig. 13

Frequency–response curves for different values of spring stiffness: s=2,ξ1=0.1,ξ2=0.9,α11=α12=0.01,α21=α22=0.1,γp=kp/6,f=5,μ=0.2

Grahic Jump Location
Fig. 14

Frequency–response curves for different values of damping: s=2,ξ1=0.1,ξ2=0.9,α11=α12=0.01,α21=α22=0.1,kp=2π4,γp=kp/6,f=5,μ=0.2

Grahic Jump Location
Fig. 15

Frequency–response curves for a conductor with one and two dampers (no damping): s=2,ξ1=0.1,ξ2=0.9,α11=α12=0.01,α21=α22=0.1,kp=2π4,γp=kp/6,μ=0.2,f=5

Grahic Jump Location
Fig. 16

Frequency–response curves for a conductor with one and two dampers (with damping cdp = 50): s=2,ξ1=0.1,ξ2=0.9,α11=α12=0.01,α21=α22=0.1,kp=2π4,γp=kp/6,μ=0.2,f=5

Grahic Jump Location
Fig. 17

Frequency–response curves for a conductor with one and two dampers (with damping cdp = 10): s=2,ξ1=0.1,ξ2=0.9,α11=α12=0.01,α21=α22=0.5,kp=2π4,γp=kp/6,μ=0.2,f=5

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