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TECHNICAL PAPERS

Forced Vibration Analysis of an Elevator Rope With Both Ends Moving

[+] Author and Article Information
Hiroyuki Kimura

Toshiba Corporation, Power and Industrial Systems R&D Center, 1, Toshiba-cho, Fuchu-shi, Tokyo, 183-8511 Japanhiroyuki4.kimura@toshiba.co.jp

Hiroaki Ito

Toshiba Corporation, Power and Industrial Systems R&D Center, 1, Toshiba-cho, Fuchu-shi, Tokyo, 183-8511 Japanhiroaki3.ito@toshiba.co.jp

Yoshiaki Fujita

Toshiba Corporation, Power and Industrial Systems R&D Center, 1, Toshiba-cho, Fuchu-shi, Tokyo, 183-8511 Japanyoshiaki1.fujita@toshiba.co.jp

Toshiaki Nakagawa

Development Department, Toshiba Elevator and Building Systems Corporation, 1, Toshiba-cho, Fuchu-shi, Tokyo, 183-8511 Japantoshiaki2.nakagawa@toshiba.co.jp

J. Vib. Acoust 129(4), 471-477 (Feb 21, 2007) (7 pages) doi:10.1115/1.2748471 History: Received June 06, 2006; Revised February 21, 2007

An elevator rope for a high-rise building is forcibly excited by the displacement of the building caused by wind forces. Regarding the rope, there are two boundary conditions. In the first case, one end moves with time and the other end is fixed, while in the second case, both ends move with time. A theoretical solution to the forced vibration of a rope where one end is moving has been already obtained. In this paper, a theoretical solution to the forced vibration of a rope where both ends are moving is presented, based on the assumption that rope tension and movement velocity are constant, and that the damping coefficient of the rope is zero or small. The virtual sources of waves, which can be assigned to reflecting waves, are used to obtain the theoretical solution. Finite difference analyses of rope vibration are also performed to verify the validity of the theoretical solution. The calculated results of the finite difference analyses are in fairly good agreement with that of the theoretical solution. The effects of the changing rate of rope length and the damping factor on the maximum rope displacement are quantitatively clarified.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Simulation model

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Figure 2

Lattice point (upper end)

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Figure 3

Propagation waves of rope

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Figure 4

Time history of rope displacement (N0=50, α=0.5, β=0.25, ς=0.0, and Us=u0sin2πτ)

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Figure 5

Time history of rope displacement (N0=200, α=0.5, β=0.25, ς=0.0, and Us=u0sin2πτ)

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Figure 6

Time history of rope displacement (N0=200, α=0.5, β=0.25, ς=0.0, and Uc=u0sin2πτ)

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Figure 7

Effects of number N0 on the maximum rope displacement (α=0.5, β=0.25, ς=0.0, and Us=u0sin2πτ)

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Figure 8

Time history of rope displacement (α=0.4, β=0.2, ς=0.1, and Us=u0sin(0.75×2πτ))

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Figure 9

Response curves of rope (Us=Uc=u0sin(0.75×2πτ))

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Figure 10

Maximum rope displacement (FDM, N0=200, β=α∕2, Us=Uc=u0sin(0.75×2πτ))

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Figure 11

Effects of velocity ratio α,β on maximum rope displacement (FDM, ς=0.1, Us=Uc=u0sin(0.75×2πτ))

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Figure 12

Maximum rope displacement (FDM, N0=200, Us=Uc=u0sin(0.75×2πτ))

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Figure 13

Relation between rope length L(τAn)∕L0 and number n

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