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    Journal of Wind Engineering

    and Industrial Aerodynamics 89 (2001) 633647

    Vortex-induced cable vibration of cable-stayed

    bridges at high reduced wind velocity

    Masaru Matsumotoa,*, Tomomi Yagia, Yoshinori Shigemurab,

    Daisuke Tsushimac

    aDepartment of Global environment Engineering, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto

    606-8501, Japanb Project Engineering Department, Kawasaki Heavy Industries Ltd., 2-4-1, Hamamatsu-cho, Minato-ku,

    Tokyo 105-6116, JapancDesign Department, Bridge Division, Ishikawajima-Harima Heavy Industries, Co., Ltd., 5-17, Hikarimachi,

    Kure, Hiroshima 737-8515, Japan

    Abstract

    In this paper, mechanisms of vortex-induced vibration of inclined cables at high reduced

    wind velocity region are discussed using results from a series of wind tunnel tests. As a

    conclusion, this aerodynamic instability of inclined cables would occur by the fluid interaction

    between Karman vortex and axial vortex. Also, the axial flow along the cable axis and the

    upper water rivulet control this aerodynamic instability. Furthermore, three dimensional

    properties of vortex shedding around the cable must play important roles in these mechanisms.

    # 2001 Elsevier Science B.V. All rights reserved.

    Keywords: Inclined cables; Vortex-induced vibration; Karman vortex; Axial vortex; Axial flow;

    Water rivulet

    1. Introduction

    The reduction of wind-induced cable vibration is one of the major problems in

    designing cable-stayed bridges. There are many kinds of wind-induced cable

    vibration, such as Karman vortex excitation, galloping, rain and wind induced

    vibration, vortex-induced oscillation at high wind velocity and so on. Hikami [1]

    found the rain and wind induced cable vibration of inclined cables at the Meiko

    *Corresponding author. Tel.: +81-75-753-5091; fax: +81-75-761-0646.

    E-mail address: matsu@brdgeng.gee.kyoto-u.ac.jp (M. Matsumoto).

    0167-6105/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved.

    PII: S 0 1 6 7 - 6 1 0 5 ( 0 1 ) 0 0 0 6 3 - 0

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    Nishi Bridge, and he succeeded to reproduce the similar vibration with artificial

    precipitation in a wind tunnel. Matsumoto [2] pointed out that inclined cables can

    also oscillate under no precipitation condition and its instability caused by the axial

    flow behind the cables. Then, Matsumoto [3] clarified that the upper water rivuletand the axial flow behind the inclined cable play important roles in the galloping

    instability and also in the velocity restricted response at the high reduced wind

    velocity. However, all of the generation mechanisms of wind-induced cable

    vibrations are not always well explained yet. Especially, the mechanism for the

    velocity restricted vibration at high reduced wind velocity, which is considered as a

    sort of vortex-induced vibration, is still unknown.

    From the observation results of prototype cables, this kind of vibration always

    occurs at the reduced wind velocity V=fD=20, 40, 60, 80 and so on, where V is awind velocity, f is a frequency of vibration and D is a diameter of cable [4]. It should

    be noted that these particular wind velocities are rather higher than the resonance

    wind velocity region of Karman vortex excitation. Matsumoto [5] tried to explain the

    mechanism of this phenomenon by three dimensional interaction between Karman

    vortex and axial vortex along the cable. In this paper, the discussion is focused on the

    generation mechanism of this vortex-induced oscillation of inclined cables at high

    wind velocity, which seems to be one of the most significant problems in cable

    aerodynamics of bridges at present. To find out a solution to reduce the cable

    vibration aerodynamically or even mechanically, it is necessary to clarify this

    generating mechanism. Then, a series of wind tunnel tests were conducted, which

    were measurements of aerodynamic lift force of stationary/oscillating circularcylinders, unsteady pressure along the cylinders and flow visualization tests, as

    follows.

    2. Wind tunnel tests

    The wind tunnel used in this study is a room-circuit type, which working section is

    1.8 m height and 1.0 m width, and the maximum wind velocity is 30 m/s. A circular

    cylinder as a model of cable was installed with yaw angle in the wind tunnel. The

    mounting position of the cylinder can be defined as the vertical angle a and thehorizontal yaw angle b, see Fig. 1. Then, the relative yaw angle b* , which defines

    relative angle between the wind direction and the cable axis, can be introduced as

    follows:

    b* arcsin cos a sin b: 1

    However, in this study, the vertical angle was chosen as a 08. Therefore, the cable

    position against wind direction can be defined by only the horizontal yaw angle b.

    Then, the top view of the wind tunnel is shown in Fig. 2, and the yaw angle b and the

    distance X from the side wall are defined as in Fig. 2. Also, the diameter D of rigid

    cable model used in this study is 50 mm or 54 mm.In this series of wind tunnel tests, the total aerodynamic lift force of the cable

    model and the pressure distribution along the cable axis were measured under

    M. Matsumoto et al. / J. Wind Eng. Ind. Aerodyn. 89 (2001) 633647634

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    various conditions. The windows on both the wall of wind tunnel were opened to

    support the cable model at the both ends of cylinder, which diameter is 200 mm.

    These windows can be closed to control the end flow condition by installing so called

    end plates. In some cases, the artificial water rivulet was attached on the cable model

    as shown in Fig. 3, and the position of the rivulet is defined by the angle y from the

    stagnation point. On the cable model for measuring surface pressure, 48 pressuretaps are installed in a single line along the cable axis. Then, the position of the

    pressure hole is defined by y and X as mentioned above.

    Fig. 2. Top view of wind tunnel.

    Fig. 3. Position of artificial water rivulet.

    Fig. 1. Attitude of inclined cable.

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    Also, flow visualization tests at the wake of the cable model were done using

    smoke wire technique.

    3. Unsteady aerodynamic lift force of stationary cylinder

    The rigid circular cylinder was mounted in the wind tunnel with yaw angle b=08,

    and the total aerodynamic lift force was measured in the stationary situation. For the

    basic case, the power spectrum distribution of the lift force at the wind velocity

    V=3 m/s in smooth flow is shown in Fig. 4. There are two dominating frequency in

    the figure, the higher one corresponds to Strouhal number 0.2 and the lower one

    seems to correspond to the reduced wind velocity V=fD=20, where the vortex-

    induced oscillation may occur.The result of the case with yaw angle b=458 is shown in Fig. 5. And the case with

    additional artificial axial flow using a vacuum cleaner is also shown in Fig. 6. In both

    the cases, the lower frequency components in the above basic case move to further

    lower frequency region, which corresponds to the reduced wind speed V=fD=40.This is also the occurring reduced wind velocity of this vortex-induced oscillation.

    Therefore, the axial flow along the cable axis may have some contributions to the

    generation of the vortex-induced oscillation at higher wind velocity. Furthermore,

    the result of the case attaching end plates is shown in Fig. 7. In this case, the air flow

    cannot be supplied from the outside of the wind tunnel to the cable direction. From

    the results, the lower frequency components of the lift force seem to be totallyvanished. On the other hand the component of Karman vortex shedding is

    remarkably enhanced. Then, it becomes clear that the axial flow has an important

    role in this phenomenon of higher wind velocity region.

    Fig. 4. Power spectrum density of lift force (without end plates, V=3.0 m/s, b=08, in smooth flow).

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    To investigate the effects of the turbulence of natural wind, the measurement of

    the lift force under the turbulent flow, where the intensity Iu=12.7%, was conducted

    in the same way as previous cases. However, the lower frequency components, which

    seems to be the generation source of the vortex-induced oscillation in high wind

    speed, never tends to be enhanced, see Fig. 8.

    4. Unsteady aerodynamic lift force of oscillating cylinder

    The total aerodynamic lift force of forced vibrating cylinder was measured.

    However, due to the restriction of wind tunnel facility for this experiment, the cable

    Fig. 5. Power spectrum density of lift force (without end plates, V=3.0 m/s, b=458, in smooth flow).

    Fig. 6. Power spectrum density of lift force (with artificial axial flow, V=3.0 m/s, b=08, in smooth flow).

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    model was mounted in the wind tunnel with horizontal yaw angle b=08, instead of

    b=458. To realize the similar flow condition to the inclined state of cable, the

    artificial axial flow was applied in some cases. Also, the cable model was forced to

    vibrate in vertical direction by the frequency f0=2 Hz a