Abstract
The effect of varying the structural mode excitation on bending-dominated flexible cylinders undergoing vortex-induced vibrations was investigated. The response of the bending-dominated cylinders was compared with the response of a tension-dominated cylinder using multivariate analysis techniques. Experiments were conducted in a recirculating flow channel with a uniform free stream with Reynolds numbers between 650 and 5500. Three bending-dominated cylinders were tested with varying stiffness in the cross-flow and in-line directions of the cylinder in order to produce varying structural mode shapes associated with a fixed 2:1 (in-line:cross-flow) natural frequency ratio. A fourth cylinder with natural frequency characteristics determined through applied axial tension was also tested for comparison. The spanwise in-line and cross-flow responses of the flexible cylinders were measured through motion tracking with high-speed cameras. Global smooth-orthogonal decomposition was applied to the spatio-temporal response for empirical mode identification. The experimental observations show that for excitation of low mode numbers, the cylinder is unlikely to oscillate with an even mode shape in the in-line direction due to symmetric drag loading, even when the system is tuned to have an even mode at the expected frequency of vortex shedding. In addition, no mode shape changes were observed in the in-line direction unless a mode change occurs in the cross-flow direction, implying that the in-line response is a forced response dependent on the cross-flow response. The results confirm observations from previous field and laboratory experiments, while demonstrating how structural mode shape can affect vortex-induced vibrations.
Highlights
IntroductionThe vortex-induced vibration (VIV) of long, flexible structures is a complex problem due to the large number of variables that can contribute to the coupled response of the structure with the surrounding fluid (Sarpkaya, 2004).While a significant number of experimental studies have been devoted to characterizing the fundamental fluid-structure interaction for an elastically mounted rigid circular cylinder undergoing vortex-induced vibrations (Bearman, 1984; Sarpkaya, 2004; Williamson and Govardhan, 2004; Bearman, 2011), the spanwise effects of flexible structures have been more difficult to quantify due to the complexity of additional variables associated with flexible, continuous systems that are capable of multi-modal responses.In the single degree of freedom spring-mass-dashpot model for vortex-induced vibrations, the forcing function resulting from vortex shedding may be represented as a phase shifted harmonic function to the first order approximation (Sarpkaya, 2004)
While a significant number of experimental studies have been devoted to characterizing the fundamental fluid-structure interaction for an elastically mounted rigid circular cylinder undergoing vortex-induced vibrations (Bearman, 1984; Sarpkaya, 2004; Williamson and Govardhan, 2004; Bearman, 2011), the spanwise effects of flexible structures have been more difficult to quantify due to the complexity of additional variables associated with flexible, continuous systems that are capable of multi-modal responses
If one considers a uniform distribution of force over the span of the beam, where the force is a harmonic function applied with a frequency equal to the second mode natural frequency, one finds that the spanwise response will have a symmetric shape similar to the shape observed in the present experiments
Summary
The vortex-induced vibration (VIV) of long, flexible structures is a complex problem due to the large number of variables that can contribute to the coupled response of the structure with the surrounding fluid (Sarpkaya, 2004).While a significant number of experimental studies have been devoted to characterizing the fundamental fluid-structure interaction for an elastically mounted rigid circular cylinder undergoing vortex-induced vibrations (Bearman, 1984; Sarpkaya, 2004; Williamson and Govardhan, 2004; Bearman, 2011), the spanwise effects of flexible structures have been more difficult to quantify due to the complexity of additional variables associated with flexible, continuous systems that are capable of multi-modal responses.In the single degree of freedom spring-mass-dashpot model for vortex-induced vibrations, the forcing function resulting from vortex shedding may be represented as a phase shifted harmonic function to the first order approximation (Sarpkaya, 2004). While a significant number of experimental studies have been devoted to characterizing the fundamental fluid-structure interaction for an elastically mounted rigid circular cylinder undergoing vortex-induced vibrations (Bearman, 1984; Sarpkaya, 2004; Williamson and Govardhan, 2004; Bearman, 2011), the spanwise effects of flexible structures have been more difficult to quantify due to the complexity of additional variables associated with flexible, continuous systems that are capable of multi-modal responses. The force in phase with acceleration alters the effective mass of the system, while the fluid force in phase with velocity alters the effective damping of the system. Using integral quantities of the forces in phase with velocity and acceleration, one can consider the system to have an effective natural frequency that is dependent on the fluid force in phase with acceleration
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