The Seventh Asia-Pacific Conference on Wind Engineering, November 8-2, 2009, Taipei, Taiwan WIND-INDUCED VIBRATION OF SLENDER STRUCTURES WITH TAPERED CIRCULAR CYLINDERS Delong Zuo Assistant Professor, Wind Science and Engineering Research Center, Department of Civil and Environmental Engineering, Texas Tech University Lubbock, Texas, USA, delong.zuo@ttu.edu ABSTRACT Circular cylindrical members of structures are known to be susceptible to wind excitations. Previous investigations have primarily focused on cylinders with uniform cross-sections. In this paper, the aeroelastic behavior of tapered circular cylinders in both uniform and sheared flow are studied based on full-scale observations. Two types of excitation mechanisms, one associated with low wind speed and the other with high wind speed, were identified. KEYWORDS: TAPERED CIRCULAR CYLINDER, VORTEX SHEDDING, BUFFETING, VIBRATION Introduction Circular cylinders are often used as slender structural elements, such as stay cables of cable-stayed bridges, chimney towers, and the mast arm of traffic-signal-support structures. Many of these elements are known to be susceptible to various types of wind-induced oscillation. For example, tall chimneys of circular cross-section are prone to vibrate due to vortex shedding (e.g., Kawecki and Zuranski 2007; Vickery and Basu 984), and stay cables have been observed to vibrate at excessive amplitude under rain-wind excitation. (e.g. Matsumoto et al. 200; Zuo et al. 2008). Previous study have primarily focused on problematic vibrations of circular cylinders with uniform cross-section. Oscillations of tapered circular cylinders were sometimes either overlooked or associated with aerodynamic instability of other structural or non-structural elements attached to these cylinders. A typical example is wind-induced vibration of traffic-signal-support structures with cantilever tapered arms. These vibrations have traditionally been believed to be due to the interaction between the wind flow and the signal clusters or the accessories of these clusters, such as the so-called back-plate installed behind the signal lights to block sunshine for motorists. Most previous studies suggested that the vibrations were due to galloping of signal lights of particular configurations (e.g., Dexter and Ricker 2002; Kaczinski et al. 998; Pulipaka et al. 998), and a recent investigation postulated that vortex-shedding off the back-plates was the source of excitation (Cruzado 2007). However, the mitigation devices developed based on these previous understandings, such as impact dampers (e.g., Cook et al. 200; McManus 2000) and aerodynamic modification of various types to, or around, the signal lights (Pulipaka et al. 998), has been observed to be either ineffective or inefficient. This indicates that the understandings of the excitation mechanisms centered at the traffic-signals was potentially. Based on full-scale measurement of two structures, this research studies the aerodynamics of tapered circular cylinders and its role on the problematic vibration of structures with such structural members.
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-2, 2009, Taipei, Taiwan Methodology The two structures subjected to study are a traffic-signal-support structure and a lighting pole, both having tapered circular cylinders as main structural members. The steel traffic-signal-support structure consists of a 5.97 m tapered pole of 5 m and 0.47 m in outer diameter at its base and at upper end, respectively, and a 8.29 m tapered cantilever arm of 0.470 m and 0.262 m in diameter at its connection with the pole and at free end, respectively. Figure shows a picture of this structure, and Figure 2 shows schematically the top view of the structure and the four signal clusters attached. During the first stage of the study (November, 2007 to January, 2009), the signal clusters and the road sign, but not the aerodynamic damper near the tip of the arm, were attached. During the second stage (January to August, 2009), all attachments were removed. Three tri-axial accelerometers were used to monitor the oscillation of the structure: one at the tip and one at the mid-span of the arm, and the other at the upper end of the pole. The wind at the site was measured by an ultrasonic anemometer mounted at the top of an adjacent smaller traffic-signal-support structure, which is the same in height as the structure subjected to study. This anemometer is chosen because the smaller structure only exhibited insignificant oscillations. Figure 2 also shows the coordinate system for characterization of the vibrations and the wind environment. The "Z" direction, which is not shown, follows the right-hand rule. The "X-" and "Z-" axes form the in-plane direction, and the "X-" and "Y-" axes form the out-of-plane direction of the structure. U denotes the wind vector, and represents the direction of the horizontal wind component. Figure Traffic-signal-support structure subjected to monitoring.22 m X Y 0.6 m.22 m 2.3 m.22 m Arm 2.44 m.22 m 2.44 m 6.40 m Pole U Figure 2 Top view of signal structure monitored The aluminum lighting pole consists of a 0.67 m tapered pole, which is 25 cm and 5 cm in diameter at the base and at the top, respectively. The cantilever arm has a 3.66 m spread and a.52 m rise. The main arm is a bent aluminum tube of 0.3 cm in wall thickness. The horizontal portion of the arm has a circular cross-section of 6 cm in outer diameter; the inclined portion tapers from an elliptical cross-section (. cm in major axis and 6 cm in minor axis) at the arm-pole connection to a circular cross-section of 6 cm in diameter where it turns horizontal. The arm is reinforced by an inclined strut of 3.8 cm in diameter and a vertical strut with an elliptical cross-section (3.8 cm in major axis and.7 cm in minor axis). The structure is anchored on a steel base bolted to a concrete foundation. The vibration of this
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-2, 2009, Taipei, Taiwan structure was monitored by three accelerometers: one on the luminaire, one near the top and one at approximately 2/3 height of the pole. The wind was measured by an ultrasonic anemometer in the vicinity of the pole at a height of 3.96 m above ground. Fig. shows schematically the lighting pole and the location of the accelerometers (Ac # to #3), as well as a coordinate system for characterization of the vibration and the wind. The Z direction, which is not shown, is determined by the right-hand rule. 2.36 m 3.58 m 0.06 m 3.66 m 0.8 m Y U 7. m X Figure 3 Lighting pole subjected to study, and configuration of measurement system The accelerometers and the anemometers were monitored by an onsite computer, which sampled all channels continuously at 30 Hz. The computer recorded a data file every one hour. The acceleration records were numerically integrated to estimate the corresponding displacement time histories. The displacement time histories were filtered by a fifth-order band-pass Butterworth filter to estimate the modal responses of interest. The Hilbert transform was then used to estimate the amplitude and frequency of these modal responses. Recorded data suggest that for both structures, the vibration could be highly non-stationary. Due to this reason, one-minute statistics of the vibration and the wind are presented subsequently. Interpretation of Traffic-Signal-Support Structure Vibration Table lists the natural frequencies of the first two modes of the structure, which are identified based on the recorded vibrations. According to a previous study (Cruzado 2007), the damping ratio in the first in-plane and out-of-plane modes are both about 0.25%. Table Natural frequencies of the first three modes of the traffic signal structure Mode with / without signals (Hz) Luminaire Mode 2 with / without signals (Hz) In-Plane (X-Z).00 /. 3.34 / 3.88 Out-of-Plane (X-Y) 0.93 /.04 3.86 / 4.08 With or without the signals attached, the structure only exhibited significant vibration in its first modes. Since the vibration is largest at the tip of the arm for these modes, only the first-mode displacement amplitudes at this location will be presented subsequently. Also, only segments with amplitude exceeding 0.25 cm in direction will be presented. Figure 4 (a) and (b) show the correlation between the mean in-plane amplitudes and the mean wind speeds and directions, respectively. Figure 5 (a) and (b) show the same correlation for the out-of-plane vibration. Two types of vibration can be identified: type A occurring predominantly in the in-plane direction at large amplitude over restricted wind speed (< 5 m/s) and direction ranges; type B occurring over the entire wind speed and direction ranges, with the amplitudes appearing to increase with increasing wind speed. Because the across-wind vibrations of type A occurred over a restricted range of low wind
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-2, 2009, Taipei, Taiwan speed, they might be due to vortex-shedding; Because the amplitudes of the two dimensional vibrations of type B increased with increasing wind speed, they might be due to buffeting. Type A Type A Type B Figure 4 In-plane amplitude vs. wind (a) speed and (b) direction, with signals Type B Figure 5 Out-of-plane amplitude vs. wind (a) speed and (b) direction, with signals Figure 6 (a) and (b) depict the dependence of the in-plane and out-of-plane vibrations, respectively, on reduced velocity, which was calculated based on the wind component normal to the arm and the mid-span diameter of the arm. That is, V U sin /( f D ) r, where U is the mean wind speed, f is the vibration frequency, and D is the diameter. The figures suggest that the vibrations of type A occurred over a narrow range of low reduced velocity centered at a value slightly higher than 5, the reduced velocity around which uniform circular cylinders exhibit the largest-amplitude vibration due to vortex-shedding. This is believed to be due to the facts that the cylinder diameter associated with vortex-shedding might be different D and that the Strouhal number associated with this particular tapered cylinder might be different from that associated with uniform circular cylinders. For vibrations of type B, it can be seen that as a trend the vibration amplitude increased with increasing reduced velocity. Type A Type B Type B Figure 6 (a) in-plane and (b) out-of-plane amplitude vs. reduced velocity, with signals Figure 7 presents the in-plane amplitudes against the out-of-plane ones. Figure 7 (a) represents segments associated with U 5m/s, which are primarily of type A, and Figure 7 (b) represents vibration type B. It is evident that vibration type A occurred primarily in the across-wind direction and that those of type B have significant components in both across-
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-2, 2009, Taipei, Taiwan wind and along-wind directions. This further suggests that type A was induced by vortexshedding and that type B was likely due to buffeting. (a) (b) Figure 7 In-plane vs. out-of-plane amplitudes for (a) type A and (b) type B, with signals This observation that the traffic-signal-support structure was susceptible to vortexshedding off the mast arm is contradictory to previous reports that the vibrations were primarily due to wind action on the traffic signals (e.g., Cruzado 2007; McDonald et al. 995; Pulipaka et al. 998). This can be verified by observed vibrations without the signals attached. Figure 8 and Figure 9 show dependence of the in-plane and out-of-plane vibration amplitudes, respectively, on wind speed and direction, when the signals were not attached. Two distinct types of vibration can be identified: type C occurring predominantly in the inplane direction at large amplitude over restricted wind speed (< 5 m/s) but broad wind direction ranges, and type D occurring over broad wind speed and direction ranges and appeared to have both in-plane and out-of-plane components. Type C Type D Figure 8 In-plane amplitude vs. wind (a) speed and (b) direction, without signals Type D Figure 9 Out-of-plane amplitude vs. wind (a) speed and (b) direction, without signals By comparing these figures with Figure 4 and Figure 5, it can be observed that vibrations type C and type A are similar except: () that type C occurred much more often and at larger amplitudes than did type A and (2) that type C occurred over much broader ranges of wind direction. It also can be seen that although type D and type B occurred over similar wind speed and direction ranges, they were different in: () that Type D could be more dominated
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-2, 2009, Taipei, Taiwan by in-plane oscillation while type B usually had similar amplitudes in both the in-plane and out-of-plane directions, (2) that the in-plane component of type D could attain much higher amplitudes than could the same component of vibration type B and (3) that there was no clear trend of vibration amplitude increasing with increasing wind speed for vibration type D. Figure 0 (a) and (b) show the dependence of the in-plane and out-of-plane vibrations, respectively, on reduced velocity. It is evident that type C and type A occurred over similar reduced velocity ranges. This reveals that with or without the signals, the structure was susceptible to vortex-induced vibration. The fact that these vibrations were in the in-plane direction suggests that they were indeed due to vortex shedding from the arm but not the pole. Type C Type D Type D Figure 0 (a) in-plane and (b) out-of-plane amplitude vs. reduced velocity, without signals Figure shows the correlation between the in-plane and out-of-plane amplitudes without the signals attached. Figure (a) presents the segments associated with U 5 m /s, which are primarily of type C, and Figure (b) presents the rest of the segments, which are of type D. It is evident that type C vibrations were primarily in the vertical direction, which is similar to Type A. It also can be seen that type D vibrations had significant components in both the in-plane and out-of-plane directions. It is important to note, however, that as the amplitude in the across-wind direction of vibration type D increases, the vibration became increasingly dominated by this component. This is different from vibration type B occurring with the signals attached, and different from what should be expected for buffeting-induced vibration. These portion of type D vibrations dominated by the across-wind component, therefore, are likely different from vibration type B and not due to buffeting excitation. (a) (b) Figure In-plane vs. out-of-plane amplitudes for (a) type C and (b) type D, with signals The difference can also be seen in individual vibration segments. Figure 2 and Figure 3 show the time histories and the scalograms (based on Wavelet transform) of representative segments of type B and type D, respectively. It can be seen that both the in- and out-of-plane components of type B vibration were highly unsteady, which indicates the response of the structure to wind turbulence. By contrast, the in-plane component of the type D vibration appeared to be much more steady. It can be postulated, therefore, that the signals potentially suppress, rather than enhance, the in-plane vibration. The exact mechanism that induces this vibration component without the signals, however, remains to be definitively identified.
Arm-E acc Y (g) Frequency (Hz) Arm-E acc Z (g) Frequency (Hz) Arm-E acc Y (g) Frequency (Hz) Arm-E acc Z (g) Frequency (Hz) The Seventh Asia-Pacific Conference on Wind Engineering, November 8-2, 2009, Taipei, Taiwan 0-0 30 60 90 20 0-0 30 60 90 20 Time (s) 0 Figure 2 Representative vibration segment of type B, with signals - 0 30 60 90 20 0-0 30 60 90 20 Time (s) Figure 3 Representative vibration segment of type D, without signals Interpretation of Lighting Pole Structure Vibration The lighting pole only exhibited significant vibrations in its first two modes, the estimated frequencies of which are listed in Table 2. Based on free vibration tests, the damping ratio in the first in-plane mode of the structure is approximately 0.4%. Table 2 Natural frequencies of the first two modes of the lighting pole Mode (Hz).5 0 30 60 90 20.5 Mode 2 (Hz) In-Plane (X-Z).3 3.60 Out-of-Plane (X-Y) 0.9 2.70 Figure 4 (a) and (b) present the dependence of the in-plane and out-of-plane amplitudes, respectively, on reduced velocity, V U / ( f D ) r. In this case, D is taken as the diameter of the pole at the height of the anemometer (3.96 m). The in-plane vibration is represented by vertical displacement of the luminaire and the out-of-plane vibration is represented by the displacement at the upper tip of the pole. Two distinct types of vibration can also be identified in these two figures: type E occurring over a restricted range of low reduced velocity, which was due to vortex-shedding off the pole, and type F occurring over higher reduced velocity with the amplitude increasing with reduced velocity, which is suspected to be due to buffeting response of the luminaire. 0 30 60 90 20 Time (s).5 0 30 60 90 20.5 0 30 60 90 20 Time (s) 0.8 0.6 0.4 0.2 2.5 5 0 5 0.4 0.3 0.2 0. Type F (a) Type F (b) Type E Type E Figure 4 (a) in-plane and (b) out-of-plane amplitude vs. reduced velocity for lighting pole
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-2, 2009, Taipei, Taiwan Unlike in the case of the traffic-signal-support structure, the vortex-induced vibration can occur in either the in-plane or the out-of-plane direction. Figure 5 (a) and (b) present the amplitudes of the in-plane and out-of-plane vortex-induced vibration segments, respectively, against the corresponding wind direction. It can be seen that significant in-plane and out-ofplane vortex-induced vibrations only occurred when wind approached in orthogonal directions. These are because the frequencies of the structure are different in the in-plane and out-of-plane directions and the vortices can only lock in with one frequency component. (a) (b) Figure 5 Dependence of vortex-induced vibration of the lighting pole on wind direction Conclusions Full-scale measurement data of two structures are used to illustrate the response of tapered circular cylinders to wind excitation. It was observed that such cylinders can be susceptible to vortex-induced vibration, either in uniform or sheared wind. It was also observed that these cylinders can be susceptible to a type of large-amplitude vibration at high reduced velocity. References Cook, R. A., Bloomquist, D., Richard, D. S., and Kalajian, M. A. (200). "Damping of cantilevered traffic signal structures." Journal of Structural Engineering, 27(2), 476-483. Cruzado, H. J. (2007). "Risk assessment model for wind-induced fatigue failure of cantilever traffic signal structures," Texas Tech University, Lubbock. Dexter, R. J., and Ricker, M. J. (2002). "Fatigue-resistant design of cantilevered signal, sign and light supports." NCHRP Report 469, Transportation Research Board - National Research Council, Washington DC, USA. Kaczinski, M. R., Dexter, R. J., and Van Dien, J. P. (998). "Fatigue Resistance Design of Cantilevered Signal, Sign and Light Supports." (NCHRP Report 42 - Project 0-38), ATLSS Engineering Research Center, Bethlehem, PA. Kawecki, J., and Zuranski, J. A. (2007). "Cross-wind vibrations of steel chimneys--a new case history." Journal of Wind Engineering and Industrial Aerodynamics, 95(9-), 66-75. Matsumoto, M., Yagi, T., Shigemura, Y., and Tsushima, D. (200). "Vortex-induced cable vibration of cablestayed bridges at high reduced wind velocity." Journal of Wind Engineering and Industrial Aerodynamics, 89(7-8), 633-647. McDonald, J. R., Mehta, K. C., Oler, W., and Pulipaka, N. (995). "Wind Load Effects on Signs, Luminaires and Traffic Signal Structures." Texas Department of Transportation Report No. 303-F, Wind Engineering Research Center - Texas Tech University, Lubbock, TX. McManus, P. S. (2000). "Evaluation of Damping in Cantilevered Traffic Signal Structures Under Forced Vibrations," MS Essay, University of Wyoming, Laramie, Wyoming, USA. Pulipaka, N., Sarkar, P. P., and McDonald, J. R. (998). "On galloping vibration of traffic signal structures." Journal of Wind Engineering and Industrial Aerodynamics, 77-78, 327-336. Vickery, B. J., and Basu, R. I. (984). "The response of reinforced concrete chimneys to vortex shedding." Engineering Structures, 6(4), 324-333. Zuo, D., Jones, N. P., and Main, J. A. (2008). "Field observation of vortex- and rain-wind-induced stay-cable vibrations in a three-dimensional environment." Journal of Wind Engineering and Industrial Aerodynamics, 96(6-7), 24-33.