Unsteady Aerodynamic Characteristics of Transversely Inclined Prisms Under Forced-Vibration---The Base Intensification Phenomenon


 This work, through a series of forced-vibration wind tunnel experiments, investigates the aerodynamic characteristics of square prisms subject to the transverse inclination. An aeroelastic prism was tested under different wind speeds, inclination angles, and oscillation amplitudes. Through analysis on the mean pressure distribution, local force coefficient, force spectra, and aerodynamic damping coefficient, the unsteady aerodynamic characteristics of the configuration were revealed. Empirical observations discovered the Base Intensification phenomenon, which refers to a fundamental change in the structure’s aerodynamic behaviors given any degrees of transverse inclination. Specifically, it is the intensification of the aerodynamic loading, vortical activities, and aerodynamic damping on only the lower portion of an inclined structure. The phenomenon, being almost impactless to the upper portion, is also insensitive to changes in inclination angle and tip amplitude once triggered by the initial inclination. Analysis also revealed that the origin of Base Intensification phenomenon traces back to fix-end three-dimensional effects like the horseshoe vortex, instead of the predominant Bérnard-Kármán vortex shedding. Moreover, results showed that wind speed is the decisive factor for the structure’s crosswind motions. Inside the lock-in region, structure loadings, vortical activities, and the effects of Base Intensification are significantly amplified. Beyond the range, the configuration gradually resorts to a quasi-steady linearity. Finally, results from the force-vibration tests were used for the prediction of structure response. Experimental comparison revealed that the predictions notably outperform those based on rigid tests, forecasting the actual responses with a markedly improved accuracy.


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With the continuous improvement of construction technology, modern buildings are becoming 59 increasingly slender and flexible all over the world. Consequently, the influence of wind 60 loading and wind-induced vibration on super-tall buildings are of great safety concern, 61 particularly after being remined by the recent vibration of the SEG Tower in Shenzhen. 62 Therefore, studies on the aerodynamic characteristics of super-tall buildings bear critical 63 importance. To date, much remain unexplored for the even the most canonical configurations, 64 for example the square prism. To tackle the outstanding issues, the deepening of our 65 understanding of bluff-body aerodynamics demands persistent effort.

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The aerodynamic characteristic of a structure is the key determinant to its wind-induced 68 response. In the event of excessive excitations, whether by the Vortex-Induced-Vibration 69 (VIV), galloping, or fluttering, irreversible damage may be incurred on the structure. In many 70 cases, the modes of vibration are closely associated to the aerodynamic damping, because a 71 negative aerodynamic damping will aggravate the vibration until plastic deformation.  The thorough literature review discloses a critical void in bluff-body aerodynamics, that is, 123 there is yet a study on the transversely inclined prism with the aeroelastic effect. Yet the 124 configuration is highly probable given variations of the wind attack angle. Intuitively, the 125 transverse inclination will modify the aerodynamic characteristics of structures and their 126 surrounding flow field. Perhaps the only referential effort was the one that proposed a modified 127 quasi-steady model for transversely inclined prisms [15]. However, the predicted response was 128 only acceptable for the onset of galloping but notably off thereafter. Therefore, the 129 aerodynamic characteristics brough about by transverse inclination, and the feasibility of the  This work aims to examine the aerodynamic characteristics of transversely inclined prisms.

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The unsteady aerodynamic forces acting on the model were obtained through a series of forced-134 vibration tests, and the aerodynamic characteristics of the model were analyzed under 135 representative wind speeds, inclination angles, and vibration amplitude. In composition,

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Section 1 offers the contextual information and a thorough literature review on the topic of 137 investigation. Section 2 details the methodology of the forced-vibration wind tunnel test.    where B and D were the length and width of the cross-section and H was the height (Fig. 2 ).

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The aspect ratio of the model was 18:1. The natural vibration frequency of the model was set details can be found in [9], which adopted the same testing parameters.   In the most general sense, the side faces of the model experiences suction (negative pressure).

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The sharpness of pressure gradients seems to be inversely proportional to the wind speed, In comparison to that of the right side, the pressure distribution on the left side is more The unsteady aerodynamic force coefficient in the crosswind direction can be obtained as: obtained by integrating Equation (2)  The high-speed case (Fig. 11) displays shows the local RMS is generally uniform across the 321 model height and unaffected by either α or vibration amplitude. The collapse of all self-similar 322 curves into a single curve reinforces the quasi-steady notion for this range of wind speeds.

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Another interesting observation is made on the upper half. On contrary to intuitions, the maximum RMS lift for the upper half does not occur at the free-end but immediately below.

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This observation bears critical importance and will be discussed in the subsequent sections. In the high-wind case (Fig. 13), the two peaks are well separated. The peak of lower frequency  The lock-in case (Fig. 12), by contrast, is much more complicated. At = 11 , two 344 frequencies are close to each other, and a clear merging of the peaks is observed. The merging, or the resonance, between the structure and the Bérnard-Kármán vortex shedding frequencies 346 amplifies the peak amplitude at the reduced frequency of ~0.09. With an increased vibration 347 amplitude, the second peak becomes increasingly merged into the first peak, while the 348 frequency of the latter remains unchanged, hence the name lock-in. In the ⁄ = 18% case, 349 a third peak also appears around 0.18, which is believed to be the second harmonic of the 350 primary lock-in frequency. Finally, as expected, α has minimal effects on the lock-in behavior.  where the aerodynamic damping force coefficient 1 is expressed as: Since 408 ̂= cos 2 ̇= sin 2 (8) The local damping force coefficient ( ) is The generalized damping force coefficient is The normalized damping coefficient is where = 2 ⁄ , is aerodynamic damping ratio, is the unit mass.
where is the model stiffness and is the tip response.

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Publication consent was obtained from all individual participants included in the study.