APPENDIX 5.5.D CHARACTERIZATION OF WIND LOADING OF TELESCOPES

Transcription

1 APPENDIX 5.5.D CHARACTERIZATION OF WIND LOADING OF TELESCOPES Published in SPIE Proceedings Vol. 4757, Integrated Modeling of Telescoes, Lund, Sweden, February, 7-8.

2 Characterization of Wind Loading of Telescoes George Z. Angeli *, Myung K. Cho, Michael Sheehan, Larry M. Ste New Initiatives Office, AURA Inc., 95 North Cherry Ave., Tucson AZ 8579 Gemini Observatories, 95 North Cherry Ave., Tucson AZ 8579 ABSTRACT Ground-based telescoes oerate in a turbulent atmoshere that affects the otical ath across the aerture by changing both the mirror ositions (wind induced vibrations) and the air refraction index. Although the characteristics of the atmoshere are well understood in the inertial range, the validity of the homogeneous, isotroic field assumtion is questionable inside the enclosure and in the close vicinity of the structure. To understand the effect of wind on an actual telescoe, we conducted extensive wind measurements at the Gemini South Telescoe. Simultaneous measurements were made of ressures at multile oints on the mirror surface, as well as wind velocity and direction at several locations inside and outside the dome. During the test we varied the dome osition relative to the wind, the telescoe elevation angle, the osition of windscreens in the observing slit, and the size of the oenings in the ventilation gates. The data sets have been rocessed to rovide the temoral and satial characteristics of the ressure variations on the rimary mirror in comarison to the theory of atmosheric turbulence. Our investigation is art of an effort leading to the develoment of a scalable wind model for large telescoe simulations, which describes the forces due to air turbulence on the rimary mirror and telescoe structure reasonably well even inside an enclosure. Keywords: wind buffeting, wind model, large telescoes. INTRODUCTION Considering the effects of wind in the design of the next generation giant ground based telescoes is going to be vital to ensure the success of these telescoes. As the sizes of the telescoes are getting larger and larger, the concerns of wind are getting more and more serious. The direct effect of wind is buffeting, i.e. wind inflicted deformations of the mechanical structure as well as the otical elements, like the rimary mirror. The rimary mirror deformation is esecially roblematic for large segmented mirrors, where the quality of the otical surface deends only on the stiffness of the back structure and actuators. The severe effect of wind on giant telescoes is aggravated by the fact that the larger the telescoe, the lower its resonant frequencies are. Consequently, a larger telescoe can absorb a significantly higher ercentage of wind energy than a smaller one could. The same wind also affects local seeing at the telescoe through the thermal characteristics of the local turbulence. Extensive studies have roved, that maintaining thermal equilibrium inside the dome can drastically reduce this local seeing. The straightforward way to achieve isothermal surfaces is to allow efficient ventilation of the telescoe enclosure. However, the need for ventilation must be balanced against the buffeting effects of the wind. The behavior of the turbulent atmosheric boundary layer reresenting the wind close to the Earth s surface - is reasonably well understood. The velocity fluctuations at a given oint of this turbulent layer may be considered as a suerosition of theoretical eddies transorted by the mean wind, like a standing wave can be concetualized as a suerosition of traveling waves. Each eddy is assumed to cause a velocity fluctuation at the given oint with frequency of f. By analogy to the traveling wave, a wavelength and wave number can be associated with each eddy. U πf ω λ = ; κ = = f U U Here U is the mean velocity of the wind. The hyothesis that the frozen eddies are traveling with the wind, i.e. the satial frequency (wavenumber) of turbulence κ is roortional to its temoral frequency f, was first suggested by Taylor (in []).

3 The internal structure of the turbulence layer can be understood as an energy cascading rocess. When the wind seed u or more recisely the Reynolds number (Lu/ν) characterizing the airflow - reaches a critical value, the flow becomes turbulent and large eddies aear. However, inside each eddy the seed can still be high enough to generate internal turbulence, i.e. smaller eddies. This cascading goes on until the eddy size L becomes small enough to revent further turbulence. In the laminar flow then the remaining energy is dissiated as heat. Kolmogorov s two hyotheses ([] in []) state that there is a range in size of eddies where the fluid motion is locally isotroic and deends only on the rate of energy dissiation ε in the smallest eddies. The boundaries of this inertial subrange are the inner and outer scales (l and L, resectively). π π < κ < L l In order to characterize the local structure of turbulence in the atmoshere, Kolmogorov [] in [] introduced the structure tensor. After some mathematical and hysical considerations ([] in []) [], [4], [5], the structure tensor yields the onedimensional structure function, which deends on the scalar distance r and energy transfer rate ε only, with a dimensionless scaling factor of C u. () r = C ε r D u u The structure function has a close relationshi to the auto-correlation B u () and cross-correlation B u (r) functions. D () r = [ B () B () r ] () u Bernoulli s Law imlies, that - in absence of viscous stresses, - the stochastic roerties of the ressure in a given fluid are analogous to those of the square of the velocity. According to Kolmogorov s second hyothesis, in the inertial subrange we can neglect the effect of viscosity. Invoking the same dimensional argument that resulted in the velocity structure function [4], we must consider the dimensions of the velocity square structure function, dislacement and energy transfer rate as (length) 4 /(time) 4, (length) and (length) /(time), resectively. The resulting structure function has a different scaling factor C and steeer distance deendence than the velocity structure function. D u 4 4 () r = C ε r A characteristic length of correlation L can be defined for the turbulence by means of the auto-correlation B () and crosscorrelation B (r) functions, as an integral scale [6]. L = B ( ) Actually the integral can be limited to a bounded region R as long as the cross-correlation is negligible outside of this region. By using the well-known relationshi between the structure function and the correlation functions, one can exress the integral scale with the structure function only. L B ( R) u ()r r d R = R D ()r r d () D According to the Wiener-Khinchine theorem, the ower sectral density (PSD) Φ (κ) of ressure fluctuation is the Fourier transforms of the cross-correlation function B (ρ). Following Tatarski s calculation for velocity ower sectral density as an examle [4], one can determine the ressure ower sectral density in the inertial subrange. Φ 7 ( κ) = C ε κ However, the ower content of eddies certainly does not aroach infinity with growing eddy sizes, as the Kolmogorov sectrum imlies. Based on exerimental results, von Karman suggested ower saturation outside the inertial subrange ([7] in []). In his formula, the characteristic wave number κ is related to the outer scale of the turbulence, as κ =π/l.

4 vk C vk Φ ( κ ) = 7 6 κ + κ The temoral ower sectral density of the turbulence can be calculated by using Taylor s hyothesis. Here f, the characteristic frequency equals to U/L. vk C vk t Φ t ( f ) = () 7 6 f + f There are several other fitting functions for wind ower sectral densities, like Davenort [8], Antoniou [9], Harris [6], etc. but in this work we use the von Karman sectrum for its convenience. Although it is a relatively simle function, it agrees reasonably well with the test results. The von Karman sectrum is fully defined by two arameters, the magnitude C vk t and the bandwidth f. Although it is customary to assume a Kolmogorov (or von Karman) sectrum during the design and simulation of telescoes, it is widely considered as a crude estimate only. The turbulence inside the dome is obviously not homogeneous and isotroic enough to suort Kolmogorov s hyotheses, certainly not on the scale of the mountainto environment. To imrove the aroximation, a frequency deendent multilying factor, the aerodynamic attenuation was introduced [], []. It is worth to note that eole usually choose f and f a that close to each other. A = (4) + f f a The integration of the Gemini South telescoe rovided an excellent oortunity to conduct extensive wind velocity and ressure measurements in an existing large telescoe dome. Besides actual engineering interests like determining the resonse of Gemini structure on wind buffeting, or develoing a rocedure to set the wind gates on that articular enclosure, - our objective was to verify and ossibly imrove our current understanding of wind loading of telescoes, as well as to work toward a scalable telescoe wind model. Some of the results of these measurements were reorted earlier [], [], [4]. Our articular interest in our investigation resulted in this aer was to find out whether the wind buffeting of the rimary mirror was mainly influenced by the outside environment, the enclosure, or local features on and around the mirror. By identifying the source we may get a ste closer to actually redicting at least a worst-case wind scenario for telescoe designs and simulations. 4. MEASUREMENT SETUP AND DATA REDUCTION Although during the measurement camaign at Gemini South Telescoe a large amount of wind velocity and ressure data was collected, in this work we mainly focus on the ressure distribution measurements on the rimary mirror. The details of the data collection were described by Cho et al. []. Here we reeat only the most relevant information necessary to understand our conclusions. The measurements were taken inside the Gemini dome, in an environment where the wind was controlled by large wind gates (Figure.). At the time of the measurements the glass rimary mirror was not installed yet, but there was a steel dummy instead in lace. It was covered by lywood to rovide a continuous surface. The ressure sensors were installed on this lywood layer according to the configuration shown in Figure. The x-axis of the Cartesian coordinate system is arallel to the elevation axis of the telescoe with y-axis ointing uward when the telescoe is ointed toward the horizon. The actual 4

5 environment of the rimary mirror is shown in Figure. The stray light baffle is clearly noticeable in the icture, together with the mirror cover. Figure. Gemini enclosure with large ventilation gates to allow natural ventilation with ambient air Data was taken with 6 bit resolution at Hz samling rate. The total length of each measurement was 5 minutes that resulted in samling oints. The detection limit (S/N ratio ) of the ressure sensors is 8 mpa with full range of Pa. Figure. The Gemini rimary mirror and its environment 5

6 Velocity sensors (three-dimensional ultrasonic anemometers) were also laced at different locations: (i) on the edges of the rimary mirror at +X, -X, +Y and Y ositions; (ii) at the secondary mirror; and (iii) on to of the dome. The dome sensor detected the outside wind velocity for reference uroses. In the cases considered in this aer, the ambient wind velocity was ranging from 8m/s to m/s. The data sets collected have a unique label, for examle c96oo. The first letter shows the date it was collected, the first three numbers the wind direction and the last two numbers the telescoe zenith angle. The tailing two letters indicates the osition of ventilation gates: in the examle both sides are oen. In all cases described in this aer the windshield and shutter are both oen leaving the observing slit unobstructed. The temoral behavior of the turbulence on the rimary mirror is characterized by the ower sectral densities of the time series collected from each sensor. To estimate the ower sectral densities we used Welch s method [5]. This technique divides the entire time series in sections with length of 56 samles and 5 % overla, each section is windowed with a Hamming window, and indeendent eriodograms are calculated for each. The final estimate is the average of these eriodograms X Y 4 Figure. Pressure sensor locations on the dummy rimary mirror To characterize the satial correlations in the samles, we have used structure functions. Each structure function was directly calculated following the definition by grouing together the sensor airs with a given distance. Although from a strictly mathematical oint of view the structure function is defined on homogenous and isotroic fields, we alied its definition on the turbulent field inside the dome to visualize the analogy and also the differences between inside and outside ressure fields. It should be understood that the structure function averaged over the whole mirror surface is only a global measure of correlation and conceals highly turbulent local effects. The mean ressure value on the rimary mirror is certainly not constant as it would be exected outside of the enclosure and is rather deterministic with significant cross-correlation over the whole area. Since our objective was to investigate the random attributes of turbulence, we excluded the mean values from our calculations. Earlier [], when we were mainly interested in the deformation of the mirror, we reorted the structure functions incororating the mean values.. RESULTS Looking at the ressure ower sectral densities, one can recognize evident differences between high and low wind conditions (Figures 4. and 8.). The characteristic differences are clearly recurring, so it s reasonable to discuss the features of the ower sectral densities individually for oen and closed ventilation gates... Power sectral densities for high winds When both the windshield and the ventilation gates are oen, there is significant wind inside the enclosure. While the mean wind velocity outside the dome is fairly stable, on the edges of the mirror surface it varies widely, deending on the wind direction relative to the dome as well as the zenith angle of the telescoe. In the general case, when the wind is blowing on the mirror from an arbitrary direction, the flow field is quite comlex and it is rather difficult to identify common atterns. In other words, the local effects of the mirror and mirror suort system are seemingly covering u the background turbulence. 6

7 Since the detailed velocity distribution on the mirror surface is not available, these local erturbations cannot be extracted from the data to better understand the global (background) effects. We calculated the ressure ower sectral densities for all of the sensors in numerous measurement series detected under various conditions like wind direction and mean velocity, telescoe elevation and ventilation gate osition. For all tests carried out under high wind conditions, i.e. with oen gates, the PSD fits surrisingly well to the theoretical von Karman curve (Equation.). The roll-off sloe corresonds to the (-7/) Kolmogorov law with varying bandwidth (f ) at different areas and under different test conditions (Figure 4.). To recognize ossible atterns, let us consider a relatively simle case, when the telescoe is ointing to zenith, i.e. the rimary mirror is horizontal, and the wind blows from (-Y) direction (Figures 5. and 6.). In this configuration we can assume a wind velocity and direction that is fairly constant over the mirror surface. Indeed, the anemometers at (+X) and (-X) osition detected similar values (. m/s and.6 m/s) with similar (close to +Y) directions. Even for this setu, the mean ressure on the mirror is far from being constant. However, the RMS ressure lot indicates a noticeable searation between local effects and a more evenly distributed background. It is remarkable that the RMS ressure calculated without considering the mean values is significantly higher than the mean ressure itself, which imlies high turbulence. PSD [Pa /Hz] - PSD [Pa /Hz] measurement von Karman fit - - Frequency [Hz] - measurement von Karman fit - - Frequency [Hz] Pressure sensor # Pressure sensor #9 Figure 4. Pressure ower sectral densities on the rimary mirror with von Karman fit (Data set coo). The turbulence on the mirror can be characterized with the arameters of the curve fit corresonding to Equation., i.e. with the magnitude C t vk and bandwidth f. Indeed, the arameter mas show high energy content without significant turbulence (bandwidth) in the negative ressure area (sensors#8, #4 and #9), which robably indicates a local maximum in tangential wind velocity. On the other hand, there is a highly turbulent area right behind the baffle column, as it aears on the bandwidth lot. Our assumtion is that a characteristic length L - virtually an outer scale - can be derived from the bandwidth f of the background turbulence. This length calculated from the bandwidth average of the background area with the assumtion of.5 m/s wind seed is about meter. The characteristic length corresonding to the highly turbulent sot behind the baffle is 7. meter. In another case we investigated the telescoe zenith angle was 6 o with wind blowing sideways, (-X) direction. The mean wind flow was arallel to the mirror surface and reasonably constant, as the anemometers indicated. The gain and bandwidth attern on the mirror is fairly similar to the horizontal case, excet the bandwidth values are significantly higher (Figure 7.) and the attern is rotated due to the different wind direction. The rotation is less than the exected 9 o because the wind is not comletely horizontal; it has a slight elevation angle. The bandwidth values are just artly higher due to larger mean velocities (8.5 m/s and 8. m/s at +X and X ositions, consecutively). The characteristic length of the turbulence is significantly smaller: the background turbulence corresonds to about meter. The high turbulent area behind the baffle yields a characteristic length of.8 meter. 7

8 Mean ressure (ranging from to Pa) RMS ressure (ranging from to Pa) Figure 5. Pressure distribution on the rimary mirror ointing to zenith with wind direction of 9 o (+Y) (Data set coo) Y Y X X Magnitude (ranging from to Pa /Hz) Bandwidth (ranging from. to.5 Hz) Figure 6. Parameters of the best fit for ressure ower sectral densities on the rimary mirror ointing to zenith with wind direction of 9 o (+Y) (Data set coo) Y Y X X Magnitude (ranging from to 9 Pa /Hz) Bandwidth (ranging from.6 to Hz) Figure 7. Parameters of the best fit for ressure ower sectral densities on the rimary mirror with zenith angle of 6 o and wind direction of aroximately 8 o (-X) (Data set c96oo)

9 Table. Characteristic length of background turbulence on rimary mirror L U = f mean Data set (coo) Data set (c96oo) Data set (too) Data set 4 (d96oo) ZENITH ANGLE º WIND DIRECTION (+Y) ZENITH ANGLE 6º WIND DIRECTION (-X) L U mean L U mean. meter ~.5 m/s.7 meter ~ 5. m/s.4 meter ~ 8. m/s. meter ~. m/s Other data sets collected on different days with different mean wind velocities but under similar telescoe conditions yield similar numbers (Table.)... Power sectral densities for low winds The data collected with closed ventilation gates show some anomaly that needs further investigation. Many sensors detected data with PSD fitting on the Kolmogorov von Karman curves (Figure 8., sensor #). However, a significantly high number of sensors ractically the whole right side of the mirror collected data with much steeer roll-off and a tail above Hz (Figure 8., sensor #4). The figure shows a curve fit with von Karman sectrum corrected with the aerodynamic attenuation (Equation 4.). As it is clearly visible in the figure, the fit is not erfect; it estimates fairly well the increased sloe, but it does not reflect two major characteristics of the measured curve: (i) the hum around. Hz and (ii) the tail above Hz. - - PSD [Pa /Hz] - - PSD [Pa /Hz] measurement von Karman fit - - Frequency [Hz] -5-6 curve fit (von Karman & aerodynamic attenuation) measurement - - Frequency [Hz] Pressure sensor # Pressure sensor #4 Figure 8. Pressure ower sectral densities on the zenith ointing rimary mirror with week wind (Data set ccc) It is worth to note that the wind seed inside the enclosure was extremely low for this measurement. With the vent gates closed on both sides, the mean wind velocity above the mirror was.5 - m/s and the flow field was rather inhomogeneous and comlicated... Structure function The satial characteristics of the turbulence can be described with the structure function. To minimize the random effects, the temoral average of the instantaneous structure functions was calculated for the whole 5 minutes collection time. We chose to resent the square root of the structure function instead of the structure function itself (Figures 9,, and ), because the 9

10 former has a saturation level with the dimension of satial RMS ressure. Actually, the saturation level is than the temoral average of the satial RMS ressures on the mirror. times higher It is obvious from Equation. that the structure function saturates as the cross-correlation diminishes with increasing the distance between sensors. It is also obvious from the following definition of the structure function that with zero searation it goes to zero. D () r = [ ( r + r) ( )] r The correlation length defined in Equation. is clearly visible on the lots as rising distance of the structure function. The correlation lengths for the different data sets are collected in Table. Quite interestingly, the correlation length does not deend on the elevation angle of the telescoe, but it shows strong deendence on the azimuth angle. Since the mirror even with the surrounding telescoe structure seems to be fairly symmetric, it suggests that the correlation length is mainly defined by the environment of the mirror. satial.5.5 Structure function, D [Pa].5.5 Structure function, D [Pa] Sensor sacing, d [m] 7 8 Sensor sacing, d [m] Zenith angle o (data set coo) Zenith angle 6 o (data set c6oo) Figure 9. Pressure structure function on the mirror surface with wind direction of 9 o (+Y) Structure function, D [Pa] Structure function, D [Pa] Sensor sacing, d [m] 7 8 Sensor sacing, d [m] Zenith angle o (data set c45oo) Zenith angle 6 o (data set c456oo) Figure.. Pressure structure function on the mirror surface with wind direction of 5 o

11 .5 Structure function, D [Pa].5.5 Structure function, D [Pa] Sensor sacing, d [m] 7 8 Sensor sacing, d [m] Zenith angle o (data set c9oo) Zenith angle 6 o (data set c96oo) Figure. Pressure structure function on the mirror surface with wind direction of 8 o (-X) According to Simiu [6], the ratio of the characteristic and correlation lengths in turbulence is constant. L = 7.8 L Where it was ossible we derived the correlation lengths of data sets from their characteristic lengths. The results are retty close to, but slightly higher than the measured values. It is understandable though, considering that the measured structure functions contain the local turbulences that are obviously reducing the correlation, while the bandwidths were calculated only for the background. Table. Correlation length L of turbulence on the rimary mirror WIND DIRECTION 9º WIND DIRECTION 5º WIND DIRECTION 8º L data set L data set L data set o.95 meter coo. meter c45oo.8 meter c9oo zenith angle.8 meter too.7 meter t45oo o.78 meter c6oo.8 meter c456oo.9 meter c96oo zenith angle 6.88 meter d6oo.9 meter d96oo 4. CONCLUSIONS It is reasonable to conclude that the background turbulence detected on the mirror is defined by the environment of the mirror, while the local obstacles are causing turbulent effects rather limited in sace. Both the ower sectral densities and the structure functions indicate that as the wind is moving sideways i.e. its azimuth angle increasing, the airflow above the mirror is getting more turbulent; the bandwidth is increasing while the correlation length is decreasing. Although, as it was reorted earlier [], the overall RMS ressure on the mirror is higher if the mirror is ointing into the wind, the temoral bandwidth of the wind load is rather small. On the other hand, the side wind can cause considerable roblems not because of its intensity but because of its bandwidth. For a telescoe of the size of Gemini this wind buffeting frequency is still way below the resonances of the structure, but as telescoes are getting larger, the interaction is more likely. For single iece rimary mirrors like the Gemini mirror - the correlation length of ressure variations is not a significant feature, since any asymmetric load excites mainly the lowest order structural mode of the mirror, which is astigmatism [].

12 However, segmented mirrors are rone to loose their continuity (hasing) if the load is highly uncorrelated, as is the case for side winds in our exeriment. From a control oint of view a high bandwidth highly uncorrelated wind load on a segmented rimary mirror can ose a substantial challenge. It is worth noting that the correlation length we measured at Gemini is about the size of the mirrors most of the lanned extremely large segmented mirror telescoes consider. For these telescoes, either the rimary mirror control system, or the enclosure, or rather both should be designed with this fact in mind. Since any structural element or baffle inside the rimary mirror area is likely to generate high bandwidth, local turbulence, the need for them should be carefully balanced. The increased frequency of wind buffeting even on relatively small areas may cause unwanted resonances in extremely large telescoes. In this aer we considered the cases where we could estimate the wind velocity distribution on the rimary mirror from the measurements taken at the edges of the mirror. To searate local and global (background) effects in the general case when the wind blows on the mirror in an arbitrary angle, further investigation is necessary. Comutational fluid dynamics (CFD) simulations can redict the velocity distribution above the mirror, which in turn yields the ressure distribution. CFD simulations could also estimate the local turbulence due to obstacles. ACKNOWLEDGEMENTS The authors would like to acknowledge the suort of the Gemini staff on Cerro Pachon in setting u and erforming the wind tests, articularly John Roberts, Gabriel Perez, Pedro Gigoux, Manual Lazo, and Pablo Prado. We would like to thank Dr. David Smith of MERLAB for organizing the dynamic measurements and collaborating in the data reduction. Secial thanks are also extended to Dr. Oleg Likhatchev for his helful comments and suggestions. The New Initiatives Office is a artnershi between two divisions of the Association of Universities for Research in Astronomy (AURA), Inc.: the National Otical Astronomy Observatory (NOAO) and the Gemini Observatory. NOAO is oerated by AURA under cooerative agreement with the National Science Foundation (NSF). The Gemini Observatory is oerated by AURA under a cooerative agreement with the NSF on behalf of the Gemini artnershi: the National Science Foundation (United States), the Particle Physics and Astronomy Research Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), CNPq (Brazil) and CONICET (Argentina). REFERENCES [] S. K. Friedlander and L. Toer, Turbulence - Classic Paers on Statistical Theory, (Interscience Publishers, Inc., New York, 96). [] A. N. Kolmogorov, "The Local Structure of Turbulence in Incomressible Viscous Fluid for Very Large Reynolds Numbers," Comtes rendus de l'academie des sciences de l'u. R. S. S., -5 (94). [] S. F. Clifford, Laser Beam Proagation in the Atmoshere, J. W. Strohbehn, ed., (Sringer-Verlag, Berlin, 978). [4] V. I. Tatarski, Wave Proagation in a Turbulent Medium, (McGraw-Hill, New York, 96). [5] G. K. Batchelor, The Theory of Homogeneous Turbulence, (Cambridge University Press, Cambridge, 959). [6] E. Simiu and R. H. Scanlan, Wind Effects on Structures - An Introduction to Wind Engineering, (John Wiley & Sons, Inc., New York, 986). [7] T. von Karman, "Progress in the Statistical Theory of Turbulence," Journal of Marine Research 7, 5-64 (948). [8] A. G. Davenort, "The Sectrum of Horizontal Gustiness Near the Ground in High Winds," Journal of the Royal Meteorological Society 87, 94- (96). [9] D. A. Antoniou, "Turbulence Measurements on To of a Stee Hill," Journal of Wind Engineering and Industrial Aerodynamics 9, 4-55 (99). [] M. Ravensbergen, "Main Axes Servo Systems of the VLT," Proceedings of SPIE 99, (994).

13 [] I. Linares, J. Carlos, and C. Hude, "Overview of the Gran Telescoio Canarias Global Model Simulation," Proceedings of SPIE 44, (). [] Cho, Myung, Ste, Larry and Kim, Seongho., "Wind Buffeting Effects on the Gemini 8m Primary Mirrors," Proceedings of SPIE 4444, -4 (). [] Smith, David, Weech, Keith, Teutsch, Johann, Avitabile, Peter, Gwaltney, Geoff, Sheehan, Mike, and Cho, Myung. Comarison of Pressure Measurements and Oerating Data for Wind Excitation of Telescoe Structures.. Proceedings of the 9th International Modal Analysis Conference. Kissimmee, FL [4] Avitabile, Peter, Weech, Keith, Smith, David, Gwaltney, Geoff, and Sheehan, Mike. Modal and Oerating Characterization of an Otical Telescoe.. Proceedings of the 9th International Modal Analysis Conference. Kissimmee, FL [5] Signal Processing Toolbox User's Guide, (The MathWorks, Inc., ).