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TECHNICAL PAPERS

Vortex-Induced Vibration Characteristics of an Elastic Square Cylinder on Fixed Supports

[+] Author and Article Information
Z. J. Wang

Department of Mechanical Engineering,  The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Y. Zhou1

Department of Mechanical Engineering,  The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kongmmyzhou@polyu.edu.hk

1

Corresponding author.

J. Fluids Eng 127(2), 241-249 (Sep 27, 2004) (9 pages) doi:10.1115/1.1881693 History: Received February 18, 2004; Revised September 27, 2004

Abstract

The vortex-induced structural vibration of an elastic square cylinder, on fixed supports at both ends, in a uniform cross flow was measured using fiber-optic Bragg grating sensors. The measurements are compared to those obtained for an elastic circular cylinder of the same hydraulic diameter in an effort to understand the effect of the nature (fixed or oscillating) of the flow separation point on the vortex-induced vibration. It is found that a violent vibration occurs at the third-mode resonance when the vortex-shedding frequency coincides with the third-mode natural frequency of the fluid-structure system, irrespective of the cross-sectional geometry of the cylinder. This is in distinct contrast to previous reports of flexibly supported rigid cylinders, where the first-mode vibration dominates, thus giving little information on the vibration of other modes. The resonance behavior is neither affected by the incidence angle $(α)$ of the free stream, nor by the nature of the flow separation point. However, the vibration amplitude of the square cylinder is about twice that of the circular cylinder even though the flexural rigidity of the former is larger. This is ascribed to a difference in the nature of the flow separation point between the two types of structures. The characteristics of the effective modal damping ratios, defined as the sum of structural and fluid damping ratios, and the system natural frequencies are also investigated. The damping ratios and the system natural frequencies vary little with the reduced velocity at $α=0deg$, but appreciable at $α⩾15deg$; they further experience a sharp variation, dictated by the vortex-shedding frequency, near resonance.

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Figures

Figure 1

Experimental arrangement

Figure 2

Empirical correlation between Yrms and εy,rms: (a) circular cylinder (data from (18)) and (b) square cylinder at α=0deg

Figure 3

Dependence on Ur of the vibration amplitude of the square cylinder: (a) Yrms∕d and (b) Xrms∕d

Figure 4

(a) Y spectrum EY, (b) X spectrum EX, (c) u spectrum Eu (square cylinder, α=0deg, Ur≈40. The hot wire was placed at x∕d=2 and y∕d=1.5.)

Figure 5

Dependence on Ur of Yrms∕d and Xrms∕d of the circular cylinder

Figure 6

(a) Y spectrum EY, (b) X spectrum EX, (c) u spectrum Eu (circular cylinder, Ur≈26. The hot wire was placed at x∕d=2 and y∕d=1.5.)

Figure 7

Cross-flow effective damping ratios of the fluid-square-cylinder system: (a) ζy,e(1) and (b) ζy,e(3)

Figure 8

Inline effective damping ratios of the fluid-square-cylinder system: (a) ζx,e(1) and (b) ζx,e(3)

Figure 9

Dependence on α and Ur of (a) fy(1) and (b) fx(1) associated with the square cylinder

Figure 10

Dependence on α and Ur of (a) fy(3) and (b) fx(3) associated with the square cylinder

Figure 11

Power spectra for a range of Ur (square cylinder, α=0deg). The lines are drawn to highlight the trend.

Figure 12

Variation of fy(3) and fs with Ur around resonance (square cylinder, α=0deg)

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