Ambient Vibration Tests and Modal Identification of Structures by FDD and 2DOF-RD Technique

Transcription

1 T--a- Ambent Vbraton Tests and Modal Identfcaton of Structures by FDD and DOF-RD Technque Yuko TAMURA, Lngm ZHANG, Akhto YOSHIDA 3, Shnj NAKATA 4 and Takayosh ITOH 5 and 3 Tokyo Insttute of Polytechncs, Kanagawa 43-97, JAPAN E-mal: yuko@arch.t-kouge.ac.jp and yoshda@arch.t-kouge.ac.jp Nanjng Unversty of Aeronautcs & Astronautcs, Nanjng, CHINA E-mal: lmzae@nuaa.edu.cn 4 Asahkase Corporaton, Tokyo , JAPAN 5 Tokyo Electrc Power Servces, Tokyo -, JAPAN ABSTRACT: The dynamc characterstcs of structures are evaluated rather frequently by measurng ther vbratons. Ths s done to nvestgate wnd vbratons of hgh-rse buldngs or for other purposes. However, few vbraton evaluatons have focused on changes n the structural propertes of buldngs or on the rgdty of man structures and non-structural walls durng constructon. Ths paper descrbes changes of the dynamc characterstcs of a 5-story offce buldng n four constructon stages from the foundaton stage to completon. The structural propertes of each constructon stage were modeled as accurately as possble by FEM, and evaluaton of the stffness of man structural frame and comparng these FEM results wth measurement results performed non-load-bearng elements. Full-scale measurements were also carred out on hgh-rse chmney, and good correspondence was shown wth vbraton characterstcs obtaned by the DOF-RD technque and the Frequency Doman Decomposton method.. Introducton Dynamc characterzaton of cvl engneerng structures s becomng ncreasngly mportant for dynamc response predcton, fnte element modal updatng and structural health montorng, as well as for passve and actve vbraton control of buldngs, towers, long-span brdges, etc. The dynamc characterstcs of a structure can be obtaned by tradtonal expermental modal analyss. Ths requres artfcal exctaton and measurement of both responses and exctaton forces. Many cvl engneerng structures can be adequately excted by ambent (natural) exctatons such as wnd, turbulence, traffc, and/or mcro-sesmc tremors. Ambent modal analyss based on response measurements has two major advantages compared to tradtonal analyss. One s that no expensve and heavy exctaton devces are requred. The other s that all (or part) of the measurements can be used as references, and mult-nput mult-output technques can be used for modal analyss, thus enablng easy handlng of closely-spaced and even repeated modes. Ths paper ntroduces a research project launched for expermental modelng of a newly desgned and constructed 5-story offce buldng by ambent modal analyss. Ambent response measurements of the CFT buldng n the feld at dfferent constructon stages were planned n order to nvestgate the varaton of ts dynamc characterstcs durng constructon. Ths was done n order to examne the separate contrbutons of the steel frames, the column concrete, the floor slabs, the external walls, the nternal walls, etc., to the buldng s dynamc characterstcs. Detectng the change n the dynamc characterstcs wth the addton of structural members or archtectural parts enabled more accurate quanttatve evaluaton of the --

2 contrbuton of these members and parts to the analytcal fnte element model (FEM) of the buldng. Another research project on ambent response feld measurements of hgh-rse steel chmney s also reported, where the dynamc characterstcs are obtaned by frequency doman decomposton (FDD) and a newly proposed DOF-RD technque.. Dynamc Characterstcs of 5-Story Offce Buldng [][]. Tested CFT Buldng The buldng tested s a mddle-rse 5-story offce buldng 53.4 m hgh, located n Ichgaya, Tokyo. It extends from 6.m underground to 59.5m above basement level, as shown n Fgure. It has one story beneath ground level and 5 stores above. The columns are concrete-flled-tube (CFT), as shown n Fgure, and the beams are wde-flange steel. The floor comprses a concrete slab and steel deck. The exteror walls of the frst floor are of precast concrete. The walls from the second floor to the top are of autoclaved lghtweght concrete (ALC). The ALC exteror walls are attached by a half lockng method. The nteror walls are attached by the slde method. The plan of a standard story s.m long by 3.8m wde, and the floor-to-floor heght s 3.8m. The ples are under the foundatons, and the underground story are of SRC (steel-encased renforced concrete). When the steel frame porton was erected up to the th floor, the CFT columns were flled wth concrete. The concrete was placed by the pressng method from the frst floor pedestal porton. After that, the steel frame was erected up to the 5th floor, and the floor slab concrete was placed after the concrete was placed n the CFT columns. The concrete strengths were 5.9m 3.8m 4N/mm underground, 4N/mm for the column fllng, and N/mm (lghtweght concrete) above ground.. Feld Measurement Feld ambent response measurements were conducted at four dfferent constructon stages. Fgure 3 shows the transton of constructon stages. Stages I and II measurements were conducted to compare the dynamc propertes before and after concrete fllng of the CFT columns up to the th floor. At ths pont, the floor slab concrete for each story had not yet been placed. Stage III was when the man structure of the buldng was completed. Concrete fllng of CFT columns and slab concrete placng of each story were fnshed, and the dynamc propertes of the man structure tself were checked. A tower crane was nstalled from Stage I to Stage III. Stage IV was at completon of the buldng, and the nfluence of non-load-bearng walls was checked. Servo-type accelerometers were used for ambent response measurement. Wth hgh senstvty and resoluton ( 6 V/g), a suffcent response sgnal was obtaned. The samplng rate was set at Hz, wth a Nyqust frequency of Hz. The duraton of each record was,8 seconds. 59.5m (a) Northeast (b) Northwest Fg. Elevaton of 5-story offce buldng Concrete Wde flange shapes beam Square steel ppe column Fg. Concrete-Flled-Tube (CFT) column Concrete fllng Stage I Stage II Stage III Fg.3 Transton of constructon stage Stage IV --

3 The tme seres of each channel had 36, ponts. Full ambent response measurements of the CFT buldng took less than 6 hours to fnsh wthn the same day. At Stages I, II and III, eght accelerometers were nstalled at the top of the CFT buldng, and sx accelerometers were nstalled below ground level. At Stage IV, fourteen accelerometers were used for one setup wth two accelerometers at the 5th floor as references. It s reasonably assumed that the floor was subject to lateral rgd body moton. The measured vbraton was translated nto equvalent motons at the desred corners. Accelerometers excludng reference accelerometers were used as rovng sensors for the st, nd, 3rd and 4th setups. Three accelerometers were typcally placed n the southeast (x drecton) and northeast corners (x and y drectons) from the 7th floor to 5th floor as well as n the roof. Sx accelerometers were placed at the nd, 4th and 6th floors, respectvely. The ambent data recorded durng the feld measurement was processed n the frequency doman afterwards. Power spectral densty was estmated usng full measurement data wth a frame of 4 data ponts. 5 spectrum lnes, wth frequency resoluton of.953 Hz, were calculated. A Hannng wndow was appled as usual wth 66.7 % overlap to ncrease the average number..3 System Identfcaton wth Frequency Doman Decomposton.3. Modal Frequency & Mode Shape Identfcaton Instead of usng PSD drectly, as t does by the classcal frequency doman technque, the PSD matrx s decomposed at each frequency lne va Sngular Value Decomposton (SVD). SVD has a powerful property of separatng nosy data from dsturbance caused by unmodeled dynamcs and measurement nose. For the analyss, the Sngular Value plot, as functons of frequences, calculated from SVD can be used to determne modal frequences and mode shapes. It has been proved [3] that the Normalzed Sngular Values db Hz.48Hz.9Hz (a) Stage I.4Hz (b) Stage II.48Hz.87Hz 3.93Hz 4.4Hz 4.33Hz 4.6Hz 4.Hz 4.87Hz.95Hz.86Hz.6Hz.37Hz.6Hz 4.37Hz.9Hz 4.Hz 4.6Hz peaks of a sngular value plot ndcate the exstence of structural modes. The sngular vector correspondng to the local maxmum sngular value s unscaled mode shape. Ths s exactly true f the exctaton process n the vcnty of the modal frequency s whte nose. One of the major advantages of the FDD technque s that closely-spaced modes, even repeated modes, can be dealt wth wthout any dffculty. The only approxmaton s that orthogonalty of the mode shapes s assumed. Fgure 4 presents the SV Plots of the CFT buldng at f =.76Hz f =.85Hz f 3 =.Hz -4 - (c) Stage III.85Hz.3Hz.76Hz.46Hz 3.85Hz.Hz.94Hz 4.5Hz 4.49Hz f 4 =.3Hz f 5 =.46Hz f 6 =.94Hz (d) Stage IV Fg.4 Sngular value plot at the CFT buldng f 7 =3.85Hz f 8 =4.5Hz f 9 =4.49Hz Fg.5 Mode shape of the CFT Buldng at Stage IV -3-

4 dfferent stages. Table gves nne dentfed modal frequences. Fgure 5 depcts the correspondng nne mode shapes. In the FDD technque, the PSD matrx s formed frst from ambent response measurements. ARTeMIS was used as the analyss software..3. Modal Dampng Estmaton One of the major objectves of the research project was to estmate the modal dampng of the CFT buldng. The basc dea of the FDD method s as follows [4]. The sngular value n the vcnty of natural frequency s equvalent to the power PSD functon of the correspondng mode (as a SDOF system). Ths PSD functon s dentfed around the peak by comparng the mode shape estmate wth the sngular vectors for the frequency lnes around the peak. As long as a sngular vector s found that has a hgh Modal Ampltude Coherence (MAC) value wth the mode shape, the correspondng sngular value belongs to the SDOF functon. If at a certan lne none of the sngular values has a sngular vector wth a MAC value larger than a certan lmt value, the search for matchng parts of the PSD functon s termnated. Fgure 6 gves a typcal bell of the SDOF system the frst and second modes of the CFT buldng. The remanng spectral ponts (the undentfed part of the PSD) are set to zero. From the fully or partally dentfed SDOF spectral densty functon, the natural frequency and the dampng rato can be estmated by takng the PSD functon back to the tme doman by nverse FFT as a correlaton functon of the SDOF system, as shown n Fgure 7. From the free decay functon, the natural frequency and the dampng are found by the logarthmc decrement technque. In the FDD, the power spectral densty functons should be estmated va dscrete Fourer transform (DFT) before the SVD. It s well known that leakage error n PSD estmaton always takes place due to data truncaton of DFT. Leakage s a knd of bas error, whch cannot be elmnated by wndowng, e.g. by applyng a Hannng wndow, and s harmful to the dampng estmaton Normalzed Sngular Values db Hz.85Hz Fg.6 Sngular value plot of the CFT buldng at Stage IV (Frequency ranges.5-.5hz) R(τ) / σ f =.76Hz h =.65% Tme lag τ (s) Fg.7 Correlaton functon of the st mode at Stage IV Table Natural frequency of CFT buldng Mode Dampng Rato (%) 3 st mode nd mode 3rd mode (a) st - 3rd mode.5 (%) Dampng Rato.5.5 (b) 4th - 6th mode.5 (%) Dampng Rato Natural Stage II Stage III Stage IV Stage V st nd rd th th th th th th th mode 5th mode 4th mode 7th mode.5 9th mode.5 8th mode (c) 7th - 9th mode Data Number ponts used of for FFT PSD calculaton Fg.8 Changes of dampng rato vs. data ponts at Stage IV -4-

5 accuracy, whch reles on the PSD measurements. The bas error caused by leakage s proportonal to the square of the frequency resoluton [5]. Therefore, ncreasng frequency resoluton s a very effectve way to reduce leakage error. Thanks to the volume of data taken at feld response measurements, we can afford to use more data,.e. ncrease frequency resoluton, n PSD computaton. In order to show the nfluence of the frequency resoluton on the dampng estmaton accuracy, 56, 5, 4, 48 and 496 data ponts were used to calculate the PSD functons. The correspondng frequency resolutons were.783,.39,.95,.977 and.488 Hz, respectvely. Fgure 8 presents the changes of the dampng ratos wth the number of data ponts used for PSD calculaton at Stage IV. It s very nterestng to observe that, as predcted by the theory of random data processon, the dampng ratos of all modes decrease, whle the number of data ponts, or frequency resoluton, ncrease. It appears that dampng estmates converge when the number of data ponts s large enough (reach to 496 or 89). Table shows the dampng ratos of all constructon stage wth enough data ponts to be used for PSD calculaton..4 Modal Identfcaton by FEM Analyss Mode Table Dampng Rato of CFT buldng Dampng Rato (%) Stage I Stage II Stage III Stage IV st nd rd th th th th th th FEM Model The FEM models were based on the desgn documents. For the model before fllng concrete n the CFT columns, as Stage I, the columns were of steel ppe and the CFT columns were of steel ppe portons, and the columns, whch compounded the concrete, as Stage II. For the model up to the th floor (Stages I and II), two cases were compared: the pedestal assumed as pnned, and the pedestal assumed as fxed. After the 5th floor of the buldng was completed and the slab concrete was placed, as Stage III, the feld measurement results were compared for the model wth steel floor beams and that wth composte beams. The assumpton of a synthetc beam was taken as the form where / of the length of the beam was derved from Desgn Recommendatons for Composte Constructons [6]. The underground porton was modeled as CFT columns and RC walls. The RC walls of the underground porton were modeled as shell elements. Moreover, the analyss model upon buldng completon, as Stage IV, consdered two cases: the stffness of the man structure only, and the stffness of the man structure as well as the stffness of the exteror walls. The non-load-bearng curtan walls were modeled as sprng elements, and the stffness was determned so that the frst mode natural frequency from the feld measurement agreed wth the FEM value. The general-purpose structural analyss program SAP- was used as the analyss software..4. FEM Results The vbraton modes obtaned by FEM analyss at buldng completon (Stage IV) are shown n Table. 3. In the FEM analyss, the buldng s stffness was estmated only for the members of the man structure. As a result, the FEM results are evaluated slghtly smaller than the actual values. The stffness of the buldng s exteror walls was therefore added so that the frst vbraton mode was nearly dentcal to the actual value. As a result, satsfactory agreement was obtaned up to the sxth vbraton mode. The stffness of the walls at ths stage was 9.8 kn/cm/m. Ths s reported n a paper that descrbes a survey nvestgaton on the stffness of ALC outer walls [7]. The stffness used for ths analyss s almost the same as n ths paper. The lowest natural frequency for Stage IV (at buldng completon) was measured as.76hz, where Y-dr. translatonal moton s predomnant. Survey nvestgatons of the natural perod -5-

6 of mult-story buldngs n Japan [8] show that the lowest natural frequency f (Hz) of a buldng wth a heght H (m) s approxmated by the followng expresson. H [8] f = (Steel structures ). H [8] f = (Steel encased renforced concrete structures ).5 The heght of ths buldng s 59.5m. Thus, the frequency derved from ths formula for steel structures s.85hz, and that for steel encased renforced structures s.3hz. These results show that the natural frequences of ths buldng are close to those for steel structures. Table 3 Nne mode shapes and ther natural frequences of a CFT buldng obtaned by FEM analyss and FDD (Stage IV) Mode Frequency(Hz) f f f 3 f 4 f 5 f 6 f 7 f 8 f 9 FEM Tuned FEM FDD Dynamc Characterstcs of a Chmney [9][] : Accelerometers : Sonc anemometer G.L.+m 3. Feld Measurement Set-up Ambent response measurements of a 3m- hgh chmney were conducted to nvestgate ts dynamc characterstcs. Fgure 9 shows the elevaton and plan G.L.+48m of the tested chmney, consstng of steel trusses and a concrete funnel. The chmney has an octagonal cross secton. Accelerometers were nstalled on three dfferent levels, as shown n Fg.. Two horzontal components (x, y) and one vertcal component (z) were measured at each level. A sonc G.L.+76m G.L. 3m anemometer was also nstalled at the top of the chmney. The samplng rate Fg.9 Elevaton of chmney of the acceleraton records was set at Hz, and the ambent responses were measured for 9 mnutes n total. 3. System Identfcaton by DOF-RD technque and FDD 3.. Dynamc characterstcs of chmney estmated by DOF-RD technque Fgure shows the power spectrum densty functons of acceleratons at three dfferent heghts. Peaks correspondng to several natural frequences are clearly. At frst, the general Random Decrement (RD) technque assumng a SDOF system was appled for system dentfcaton usng the ambent y-dr. acceleraton records at the top level, GL+m. By processng wth a numercal band-pass flter wth a frequency range of.6hz -.Hz, only the frequency components around the lowest peak near.4hz depcted n Fg. were extracted. The ntal ampltude of the acceleraton to get the Random Decrement N y x -6-

7 sgnature (RD-sgnature) was set at the standard devaton, σ acc. Fgure shows the obtaned RD-sgnature, where a beatng phenomenon s clearly observed, suggestng two closely located predomnant frequency components. By carefully studyng the peak near.4hz, t s seen that there are actually two peaks: at.4hz and.4hz. These peaks are named f and f, respectvely, n ths paper. The general RD technque assumng a SDOF system can effcently evaluate the dampng rato and the natural frequency only for a wellseparated vbraton mode, but not for the above case. In order to evaluate the two closely located two vbraton modes, the DOF-RD technque s proposed, where the supermposton of the two SDOF systems wth dfferent dynamc characterstcs s made. The RD sgnature shown n Fg. was approxmated by supermposton of the two dfferent damped free oscllatons as follows: R ( t) = R( t) = = x h hωt R ( t) + m e cos h ωt φ where R (t) : RD sgnature, R (t) : -th mode component ( = and ), x : ntal value of - th mode component, h : -th mode dampng rato, ω : -th mode crcular frequency, t : tme, φ : phase shft, and m : mean value correcton of RD sgnature. The approxmaton was made by the least-square method, and the dampng rato and the natural frequency of the chmney were estmated at.8% and.4hz for the st mode, and.3% and.4hz for the nd mode. The dynamc characterstcs of the 3rd and 4th modes were also estmated by the DOF-RD technque. 3.. Dynamc characterstcs of chmney estmated by FDD PSD of acceleraton S acc (f) Fg. Power spectrum of tp acceleraton (Y-dr) Acceleraton (cm/s ) Tme (s) Fg. RD sgnature of tp acceleraton (Y-dr.) The FDD method was appled to the sx horzontal components of the acceleraton responses at the three dfferent heghts to evaluate the chmney s dynamc characterstcs. Fgure shows the frequency dstrbuton of the sngular value obtaned by the FDD method. Fgure 3 s a close-up n the range of.hz -.7Hz, where the upper lne shows two peaks at.4hz and.4hz, correspondng to f and f n 3... The lower lne has a peak between.4hz and.4hz, and the rght-sde slope can be connected to the frst peak of the upper lne, and the left to the second peak. Ths forms a bell as already shown n Fg.6, so the combnaton of the upper and lower lnes can closely dentfy the located modes. Fg. 4 shows the auto-correlaton functon of the st mode obtaned by the nverse FFT for the separated peak as above. Fgure 5 shows the varatons of the dampng ratos of the lowest two modes wth the number of data ponts used for PSD calculaton. The dampng ratos converge to precse values wth ncrease n the number of data ponts. Table 3 shows the dynamc characterstcs of the chmney obtaned by the FDD method wth enough PSD data ponts and by the RD technque, where the DOF-RD technque was used for the st, nd, 3rd and 4th modes. These results show farly good agreement between the FDD and DOF-RD technques, except for the 3 rd -mode dampng rato Wdth of band pass flter.4hz.4hz. h =.8% h =.3% f =.4Hz f =.4Hz m 48m 76m 4-7-

8 Normalzed Sngular Values 4 db Hz.4Hz.47Hz.5Hz.7Hz.38Hz Fg. Frequency dstrbuton of sngular value Normalzed Sngular Values 4 db 3.4Hz.4Hz Fg. 3 Frequency dstrbuton of sngular value (Close-up: frequency range.-.7hz) Fg. 4 Correlaton functon obtaned by FDD Fg. 5 Varatons of dampng rato wth PSD data ponts 4. Concludng Remarks The dynamc characterstcs of two actual structures were estmated by the FDD and DOF RD technques usng ther ambent responses, and also by FEM. The results were all satsfactory and agreed well. R(τ)/σ Dampng rato (%) Tme lag τ (s) h =.4% f =.4Hz st mode nd mode Data ponts used for PSD calculaton Table 3 Dynamc characterstcs of chmney Mode Natural Frequency(Hz) Dampng Rato(%) RD FDD RD FDD st nd rd th th th th th References [] Tamura, Y., Zhang, L., Yoshda, A., Cho, K., Nakata, S., and Nato, S., Ambent vbraton testng & modal dentfcaton of an offce buldng wth CFT columns, th Internatonal Modal Analyss Conference, pp4-46, [] Mwa, m., Nakata, S., Tamura, Y., Fukushma, Y., and Otsuk, T., Modal dentfcaton by FEM analyss of a buldng wth CFT columns, th Internatonal Modal Analyss Conference, [3] Ibrahm, S.R. and Mkulck, E.C., A Method for the Drect Identfcaton of Vbraton Parameters from the Free Response, Shock and Vbraton Bulletn, 83-98, No. 47, Pt. 4, Sept. 977 [4] Brncker, R., Ventura, C.E. and P. Andersen, Dampng Estmaton by Frequency Doman Decomposton, Proc. of the 9th IMAC, , Feb. [5] Bendat, J. and Persol, A., <Random Data, Analyss and Measurement Procedures>, John Wley & Son, New York, USA, 986 [6] Archtectural Insttute of Japan, Desgn Recommendatons for Composte Constructons, 985 (n Japanese) [7] Fukuwa, N., Nshzaka, R., Yag, S., Tanaka, K, and Tamura, Y., Feld measurement of dampng and natural frequency of an actual steel-framed buldng over a wde range of ampltude, Journal of Wnd Engneerng and Industral Aerodynamcs, Vol.59, pp ,996. [8] Archtectural Insttute of Japan, Dampng of Structures, (n Japanese) [9] Masuda, K., Sasajma, K., Yoshda, A. and Tamura, Y., Dynamc characterstcs of a tall steel chmney. Part Ambent response measurements, Summares of Techncal Papers of Annual Meetng, Archtectural Insttute of Japan, B-, (n Japanese) [] Yoshda, A., Tamura, Y., Masuda, K. and Ito, T., Dynamc characterstcs of a tall steel chmney. Part Evaluaton of dynamc characterstcs by DOF-RD technque and FDD, Summares of Techncal Papers of Annual Meetng, Archtectural Insttute of Japan, B-, (n Japanese) -8-