EXPERIMENTAL MODAL ANALYSIS UNDER AMBIENT...

IOMAC'13 5th International Operational Modal Analysis Conference 2013 May 13-15 Guimares - Portugal

EXPERIMENTAL MODAL ANALYSIS UNDER AMBIENT EXCITATION: WHAT WE CAN LEARN FROM EXPERIENCE

Reto Cantieni

ABSTRACT This paper discusses several practical problems arising when trying to identify a civil engineering structure's natural dynamic characteristics, natural frequencies, mode shapes and damping, using modal analysis under ambient excitation procedures. Among others, it will also become clear why the expression OMA, "Operational Modal Analysis", is so imperfect that we prefer talking of AVT, "Ambient Vibration Testing". We will see that this is not perfect as well because some "artificial" support for the "ambient" excitation can be of great help. The problem here is that this "artificial" help should be of an easy and cheap nature to be produced and, of course, it should also be of broad-band nature. In addition to talking about excitation problems we will also treat problems of adapting the instrumentation layout to the needs (what do we want to know? what do we need to know? how many sensors do we need? how many references do we need? what is an optimum reference point location?, what is a reasonable number of setups?) as well as about choosing the proper digital signal properties (sampling rate?). A further topic of interest to be discussed will be how to check the quality of the results to be expected. All these problems will be discussed using tests having been performed by the author in the last 12 years, since multi-channel AVT has become operational. This also means that the problem treating schedule is not systematic. Every test being discussed here has a problem situation of its own. But, at the end of the day, most of the practical problems should have been covered.

Keywords: Experimental Modal Analysis, Ambient Vibration Testing, Civil Structure's Dynamics.

1. INTRODUCTION With traditional experimental modal analysis the structure to be identified is excited dynamically artificially, controlled, using a vibration generator. The structure's modal parameters are then derived from the time signals of input and response. Among others, practical problems arising are the choice of the driving point location, design of intensity and frequency content of the exciting force and layout of the response measurement point setups. The basic theory of "traditional" modal analysis was developed by mechanical engineers treating problems arising in the mechanical part of the engineering world (cars, aircrafts, machines etc.). These all operated in a laboratory and excitation of the structures involved was not really a problem. Hammers and shakers of all kind were easy to install and handle. Just one requirement had to be considered: The artificially generated vibration amplitudes should be much larger than those excited by ambient effects. Besides system linearity, this is one of the basic requirements of traditional modal analysis.

Session 1, Author 1, Author 2

However, when it came to civil engineering structures, the main practical problem was designing and building vibration generators with the capability of exciting the structure in an efficient way. And this requirement is difficult to fulfill for large civil structures. These tend to vibrate significantly under the action of ambient forces and a vibration generator has to be quite large to cope with these.

It is therefore not really astonishing that, after maybe 10 to 20 years of building large shakers, some dedicated civil engineers developed tools to allow system identification without using an artificial excitation. Among others, the UBC Vancouver school can be mentioned here as well as the Danish School at Aalborg University. Being an applicant of the Artemis software package since its beginning in the year 2000, the author of this paper will tell stories related to this software only. And: SSI having proved to not really being efficient, applications of the FDD (rarely) and EFDD procedures (mainly) are discussed here.

2. STEEL PLATE

2.1. Topic Can a rubber foam supported small steel plate serve as a benchmark for civil structures? No, but it shows us the high-end concerning quality an ambient modal analysis can deliver. The low-end will be discussed later: A machine foundation lying on the soil with no reasonable ambient excitation.

2.2. Steel plate (2001) The structure to be identified is a steel plate with the dimension 200 x 210 x 10 mm. Being supported by a 10 mm rubber foam layer a free-free boundary condition results. Ambient excitation is provided through continuously touching the slab with a pencil in a very light manner (Fig. 1).

The ambient test technical parameters were: 1D measurement points, 2 references, 4 rovers, 4 setups, time window: T = 10 s, sampling rate sR = 10 kHz.

Figure 1 Steel plate, instrumentation layout for setup 1. Blue: References, Nos. 17 & 18, Green: Rovers.

2.3. Ambient Excitation? Not really. Slightly touching the plate with a pencil roving all over the steel plate is artificial.

2.4. Test results Figure 2 shows the EFDD SVD diagram; the results for two modes are presented in Figure 3.

2.5. Specials: How can we check whether our measurements are good or bad? The special reason to present this steel plate test here is, to illustrating how perfect ambient modal analysis results look like (Figure 2):

Huge signal-to-noise ratio (30 dB distance between SVD-lines #1and #2!) 10 modes easily to be identified! SVD-lines #2 and #3 nicely pop up in case of "closely spaced" modes.

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5th International Operational Modal Analysis Conference, Guimares 13-15 May 2013

Figure 2 Steel Plate, EFDD SVD diagram.

Figure 3a Steel Plate, Mode 1,

f = 730 Hz, = 0.45%. Figure 3b Steel Plate, Mode 8,

f = 3'655 Hz, = 0.48%.

2.6. What can we learn? Bad EFDD SVD diagram (small distance between lines #1 and #2) reflects bad signal quality

or low signal-to-noise ratio. Which means: Either wrong sensors or bad excitation. Two references is always better than just one: The risk of both references sitting in a node of a

given mode shape is very small. Definitely smaller than the risk of the one and only reference sitting in a node of a given mode shape.

Never put a reference in the middle of anything. It will surely sit in a mode shape node. Choosing a good length of the time window per setup requires some basic knowledge of the

structure's dynamic characteristics. Rune's rule: "2'000 times the period of the structure's fundamental natural frequency". Reto's rule: "You can also survive with a 1'000 times time window". Surely, Rune can provide a scientific explanation for his rule. Reto simply relies on experience. To get an idea of a structure's fundamental period, you can perform a numerical calculation. The result of this calculation will be wrong, but you will get an idea of where this period could lie. In any case: A pilot test may always be a good idea. Because: You will get a reliable number for the structure's fundamental period.

A pilot test, being more or less free of charge in this case, tells us: The steel plate fundamental frequency is f1 = 730 Hz, the respective period is T1 = 0.00137 s, and multiplication by 2'000 results in a time window length of T = 2.74 s. Choosing T = 10 s is therefore a comfortable but cheap solution.

To illustrate the respective problem arising with really large civil structures: Ganter Bridge ([1], total length 680 m, largest span 174 m, maximum pier height 148 m) fundamental modal period T1 = 2.5 s. Multiplied by 2'000 results in a window length T = 5'000 s, which is something like 84 minutes.

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3. SHORT-TO-MEDIUM-SPAN HIGHWAY BRIDGE

3.1. Topic What is the minimum number of sensors (degrees of freedom) needed for an ambient modal analysis?

3.2. A110 bridge (2001, [2]) The problem at hand was the question, whether or not vibratory rollers can be allowed to compact a bridge's pavement. Depending on their type, such rollers produce vibrations in the f = 25...70 Hz range. The question was: Do we have bridge natural frequencies in this range prompt to being easily excited by the rollers?

The ambient test technical parameters were: 1D measurement points, 1 reference, 1 rover, 14 setups, time window: T = 105 s, sampling rate sR = 512 Hz.

Figure 4 A110 Bridge. Three spans with L = 16...20 m. Figure 5 A110 Bridge: 1DOF sensor (10 V/g).

3.3. Ambient Excitation? Being confronted with a highway bridge with a 20 m maximum span and no traffic on or below the bridge, you should do something about excitation. Because: From nothing, nothing will come. The good news with a 20 m span bridge: You will easily be in a position to exclude the walking excitation (f = 2 Hz) from the bridge's natural response (5 Hz; Figures 6, 8b).

3.4. Test results Using FDD procedures (EFDD was not yet available in 2001) 15 bridge modes could be identified in the f = 5.00133.8 Hz range (Figures 8 and 9).

Figure 6 Time signal as resulting from walking

and heel-dropping. Figure 7 Measurement point layout, Setups 1

to 14. Blue: Reference, Green: Rover.

Figure 8a FDD SVD Diagram f = 0150 Hz. Figure 8b FDD SVD Diagram f = 020 Hz.

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Figure 9 A110 Bridge: Modes No. 1 and 9.

3.5. Specials: Minimum number of sensors required? The answer is simple: Two. You then keep one of the sensors as a reference and move the other one over the structure (Figure 7). You do this especially when being a poor man not disposing of more than two sensors. As was the case with the author in the year 2000.

3.6. Specials: What could the fundamental frequency of my bridge be?

Figure 10 You are to test a highway bridge and you have no idea about its fundamental natural frequency? This figure presents this frequency as a function of the bridge maximum span ([3]). For the A110 Bridge, the 20 m span yields a frequency of something like f = 5...6 Hz. This is important because it tells us that walking and heel-dropping on the bridge will not interfere with this!

3.7. What can we learn? Every identification problem can be tackled with using just two sensors. It is however a good idea to not pass the number of 10 setups per test. Otherwise, EFDD data

processing would become quite lengthy. It is always a good idea to also measure the structural behaviour at the bearings. In many

cases, bearing points are not really fixed in space. Often, they contribute to the structure's flexibility. Here, this was not considered for the abutment bearings.

Helping the ambient excitation through walking and/or heel-dropping on a structure is a good idea if the structure's fundamental natural frequency is f > 5 Hz. Otherwise excitation and natural structural response might interfere.

4. OFFICE FLOOR

4.1. Topics Optimum number of references? "Ambient" excitation?

4.2. Mainau Office Building (2004, [4]) Office users were complaining about their computer screen shaking if a person walked through the room. This office floor is a reinforced concrete structure supported at the elevator/staircase walls and at the faade columns. Its maximum span is 7 m (Fig. 11).

The ambient test technical parameters were: 1D measurement points, 3 references, 5 rovers, 7 setups, time window: T = 300 s, sampling rate sR = 100 Hz.

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Figure 11 Mainau plan view. Figure 12 Excitation and response.

4.3. Ambient Excitation? With an office floor exhibiting a 7 m maximum span and being unoccupied, it is a good idea to overcome noise inputs from refrigerator or air conditioning systems through using an artificial excitation like a medical ball. However: Walk all over the measurement point layout and don't throw the ball at regular intervals! And keep the throwing level as constant as possible (ca. 0.5 m).

Figure 13 Time signals resulting from throwing the medical ball.

4.4. Test results Figures 14 to 16 show some of the results of this ambient modal test. They were perfect!

Figure 14 Mainau measurement point grid. The three references are not part of the measurement point grid.

Figure 15 Mainau EFDD SVD diagram.

Figure 16 Mainau modes Nos. 1 and 4.

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4.5. Specials: Minimum number of references required? With a structure consisting of several substructures, it is a good idea to have a reference in all of the substructures.

4.6. What can we learn? Artificial excitation, if adapted to the needs, may be very helpful! Harmonic artificial excitation is most probably bad. Choose something broad banded! A reference per substructure is helpful.

5. MEDIUM-SPAN RAILWAY BRIDGE

5.1. Topic What do I have to keep in mind if the goal is: FE model updating?

5.2. Erfttal Bridge (2007, [5]) The goal of the investigation presented here was generating a sound set of experimental data to allow proper updating of a bridge FE model. (The final goal was rating of the dynamic bridge behaviour under the crossing of heavy commercial and high-speed passenger trains.) The model updating challenges were: a) the open gap between the two bridge main girders is covered by the continuous ballast (Fig. 19), and, b) the bridge bearings are elastomeric pads. How should such details be modelled?

The ambient test technical parameters were: 1D measurement points, 4 references, 10 rovers, 4 setups, time window: T = 410 s, sampling rate sR = 100 Hz. The length of the time window resulted from many restrictions like total testing time available (10 am to 3 pm), the time required to rove the sensors and the no-traffic-times of this heavily trafficked bridge (Kln-Aachen Railway Line).

5.3. Ambient excitation? The heavy road traffic crossing underneath is a perfect ambient excitation for a 25-m-span bridge. The real problem to be solved here was finding a 15-minutes-window without railway traffic for each of the four setups.

Figure 17 Erfttal Bridge plan view and measurement point grid. The references are indicated in red.

(Dimensions in m.)

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Figure 19 Erfttal Bridge cross section.

Figure 18 Erfttal Bridge bottom view.

5.4. Test results Figures 20 to 22 give an impression of the results. Model updating was performed by BU Weimar.

Figure 20 Erfttal Bridge Setup 1 instrumentation. Figure 21 Erfttal Bridge EFDD SVD diagram.

Figure 22 Four Erfttal Bridge Modes. Red: Experimental, blue: Updated FE-model, black: MAC value [6].

5.5. What can we learn? FE model updating of a structure exhibiting unclear boundary conditions can only be

successful if we measure at these unclear locations: Along the open gap, at the bearings. Traffic underneath a bridge is a very nice ambient excitation.

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6. POWER HOUSE GLOBAL

6.1. Topic When is using an "operational" excitation a good idea?

6.2. Eglisau Power House (2008, [7]) All seven turbine/generator units stemming from 1905 were scheduled to be replaced (Fig. 23). As a consequence of the units rotational frequency being increased from f = 1.39 Hz to f = 1.85 Hz discussions concerning the dynamic stability of the building arose. This included the whole power house as a unit as well as its bottom part, i.e. the part covering generator and turbine units only (Fig. 24). The global modal test is discussed here, the local test in the next Chapter.

The ambient test technical parameters were: 2D measurement points, 3 references, 3 rovers, 11 setups, time window: T = 1'800 s (30 minutes), sampling rate sR = 200 Hz.

Figure 23 Eglisau Powerhouse. Seven Turbine/generator units from 1905.

As already a pilot test had shown that extraction of natural modal parameters would be very difficult with the turbine/generator units being in operation, everything was kept ready to shut down the units after pre-processing of the test with the units on (Figure 26). This happened the day after the tests with the turbines on with the whole equipment being left on site and the pre-processing having been performed during the night. In its 100 year's history all seven units had been shut down at the same time once only: During the heavy flood of 1999 when the Rhein River was carrying so much wood that everything was in danger to be destroyed. Shutting down all units was a 3 hours operation because the upstream water level has to be maintained in narrow limits: Shutting down a unit means synchronous opening of a spillway (Figure 23).

Figure 24 Eglisau Powerhouse cross section. Figure 25 Measurement point layout for Setup 2.

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6.3. Ambient excitation? The Rhein River flowing through the open spillways was a perfect source of ambient excitation!

6.4. Test results Figures 26 to 27 give an impression of the results.

Figure 26a Eglisau global EFDD SVD diagrams for

f = 0100 Hz and turbines on (above) and off (below). Figure 26b Eglisau global EFDD SVD diagrams for

f = 012 Hz and turbines on (above) and off (below).

Figure 27 Eglisau global modes Nos. 1, 2 and 4 (from the left) for the turbines being on and off.

It can be seen from the mode shapes, especially in their animated form, that the turbine/generator units are disturbing the natural modal parameters especially for low frequencies being close to the rotational frequency f = 1.39 Hz.

6.5. What can we learn? Ambient modal analysis of a structure being in normal operation can be impossible. This holds especially true if the (usually harmonic) operational vibrations start at a frequency

close to the structure's fundamental frequency. Bell towers are also a good example for this kind of problem.

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For a river exploitation system, closing down the turbine/generator units and having a significant water flow through the adjacent spillways is a very nice state of ambient excitation.

Choosing the proper number of DOF's per measurement point is important! What do we want to know?

Information will be available for the measured DOF's only!

7. POWER HOUSE LOCAL

7.1. Topic How many degrees of freedom per measurement point do we need?

7.2. Eglisau Power House (2008, [7]) The two turbine/generator units G6 and G7 were chosen for this investigation. The power house exhibits two global joints dividing the building into three well separated parts. (This also lead to the instrumentation for the global investigation as given in Figure 25.) Units G1 and G2 are the part closest to the river bank, Units G6 and G7 are located close to the river center line. A further reason for choosing the G6/G7 part of the building was the fact that these were the first to be replaced.

The ambient test technical parameters were: 3D measurement points, 2 references, 3 rovers, 12 setups, time window: T = 1'800 s (30 minutes), sampling rate sR = 200 Hz.

7.3. Ambient excitation? See Paragraph 6.3. No turbine/generator operation, the river flows through the spillways.

7.4. Test results

Figure 28 Eglisau part G6/G7 plan view. Figure 29 Measurement point layout for Setup 1.

Figure 30 Eglisau local EFDD SVD diagram for f = 016 Hz.

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Figure 31 Eglisau local modes Nos. 1 and 4.

7.5. What can we learn? The measurement degrees of freedom have to be adapted to the requirements. In this case

here: If we need information on the building floor's bending stiffness and on the foundation elasticity we also have to measure in the vertical direction.

8. MACHINE FOUNDATION

8.1. Topic Is trying to identify a machine foundation's natural modes a good idea?

8.2. Gijn Fan Foundation (2008) This paragraph focuses on the foundation of a large fan installed in a coal-fired power plant. Excessive foundation vibrations were observed with this fan being in operation. The fan fundamental frequency is f = 12.5 Hz. The fan foundation dimensions can be taken from Figure 32, some pictures are given in Figure 33.

The ambient tests technical parameters were: a) "Fan off": 1D measurement points, 1 reference, 1 rover, 6 setups, time window T = 600 s, sampling rate sR = 250 Hz. b) "Fan on": 2D measurement points, 1 reference, 1 rover, 6 setups, time window T = 600 s, sampling rate sR = 250 Hz.

Comparison of the results for the cases "Fan off" and "Fan on" is somehow tricky because the DOF's measured were not identical (due to practical reasons).

Figure 32 Gijn Fan plan view. Some measurement points are also indicated.

(Dimensions in m).

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Figure 33 The Gijn Fan. Photos from both sides.

8.3. Ambient excitation? Tests have been performed with the fan being off/on. The "ambient" test ("Fan off") took profit of a large number of further rotating machinery operating in the neighbourhood as excitation sources. One of these sources was an identical fan also rotating at f = 12.5 Hz at a distance of some 50 m.

8.4. Test results The test results are summarized in the Figures 34 to 39.

Figure 34a "Fan off" measurement point layout for all

setups. Blue: Reference DOF. Figure 34b "Fan on" measurement point layout for all

setups. Blue: Reference DOF's.

Figure 35a EFDD SVD diagram for f = 0100 Hz for

"Fan off" (above) and "Fan on" (below). Figure 35b EFDD SVD diagram for f = 020 Hz

for "Fan off" (above) and "Fan on" (below).

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Mode Freq. [Hz] Damp. [%] Shape Mode Freq. [Hz] Damp. [%] Shape

1 3.06 5.78 horizontal r.b.

1 4.10 4.17 vertical r.b.

2 4.82 2.03 vertical r.b. 2 4.81 0.34 vertical r.b.

3 5.92 0.51

3 6.61 4.40 bending 4 6.43 3.42 bending

5 8.84 3.75 bending

6 10.59 0.11 forced

4 12.48 0.29 forced 7 12.49 0.07 forced

Figure 36a Results for "Fan off". r.b. = rigid body motion.

Figure 36b Results for "Fan on". r.b. = rigid body motion.

Figure 37a Not measured. Figure 37b "Fan on"; mode 1, f = 3.1 Hz.

Figure 38a "Fan off"; mode 1, f = 4.1/4.8 Hz. Figure 38b "Fan on"; mode 2, f = 4.8 Hz.

Figure 39a "Fan off"; mode 4, f = 12.5 Hz. Figure 39b "Fan on"; mode 7, f = 12.5 Hz

8.5. What can we learn? Don't try to identify a machine foundation if no "real" sources of excitation are available. Having some machines in the neighbourhood being in operation might be helpful. Having the machine itself in operation may be helpful to identify natural modes with a

frequency lying significantly outside of the machine's harmonics (Figure 35). Don't try to interpret the shape of a mode forced at the machine's forcing frequency. This is

definitely not a natural mode.

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9. BELL TOWER

9.1. Topic Are we tackling a linear problem?

9.2. San Luzi Bell Tower (2004, 2009, 2011, 2012) San Luzi church and tower, located in Zuoz, an Engadin village, has firstly been mentioned in 1139. The oldest parts still existing stem from the 13th century. With a cross section of 5 x 5 m the bell tower is quite slender and vibrates much too intense when ringing the bells. Modal Analyses have been performed in 2004, 2009 and 2011. Since June 2012 the tower is monitored using level B 2D acceleration plus environmental instrumentation.

The ambient tests' technical parameters were: 1 1D plus 1 2D horizontal DOF's per level (3D at the foundation in 2011), 3 to 12 reference DOF's, 3 to 0 rover DOF's, 1 to 3 setups, time window always T = 1'800 s, sampling rate sR = 100 Hz. (In 2011, 14 sensors were simultaneously used in 1 setup.)

Figure 40 San Luzi Bell Tower. Photo, basic geometry and instrumentation (2011).

9.3. Ambient excitation? Of course! Wind is perfect for a tower. But stationary and ergodic? Of course not!

9.4. Test results Figure 42 gives the EFDD SVD diagrams established in 2004, 2009 and 2011. The four fundamental tower modes are always present. What we don't like are the differences in the higher frequency region (2009) and in the lower frequency region (2011). And what cannot be seen from Figure 42 are the (small but very important) differences in the frequency of the most significant mode, the first tower mode T1X. X is the ringing direction, Y is perpendicular to this (Figure 41).

2004 2009 2011

Mode Name Freq. [Hz] Damp. [%] Freq. [Hz] Damp.[%] Freq. [Hz] Damp. [%]

1 T1X 1.430 1.6 1.496 1.8 1.435 1.6

2 T2Y 1.785 1.2 1.848 2.1 1.805 1.3

Figure 41 San Luzi Bell Tower modal characteristics as of 2004, 2009 and 2011.

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9.5. What can we learn? Masonry and "old stone" structures usually exhibit a significant number of cracks and are

therefore very prone to showing a non-linear behaviour. Always keep track of wind speed and temperature. We didn't do this. We call this: Learning the hard way.

The instrumentation was too sparse to identify the mode shapes properly. The tower tip should have been included. The questions are only: How? And: Who pays the bill?

Figure 42 San Luzi f = 06 Hz EFDD SVD diagrams of the years 2004, 2009 and 2011.

10. FURTHER EXAMPLES A large wind turbine [8], an 80 m single span steel/concrete composite highway bridge [9], a 56 m steel bowstring highway bridge [10], a cable stayed footbridge [11], a dance floor and a floor in an industrial plant. For the last two examples see: www.rcidynamics.ch, projects.

11. CONCLUSIONS Think about: Excitation!? Instrumentation!? Signal-to-Noise ratio!? Time window length!? And: Never put a reference in the middle of anything!

REFERENCES [1] Felber, A., Cantieni, R. (1996) Advances in ambient vibration testing: Ganter Bridge Switzerland.

Structural Engineering International 6(3):187-190 [2] Cantieni, R., Langenegger, M. (2002) Bridge Vibrations Excited Through Vibro-Compaction of

Bituminous Deck Pavement. Proc. 5th eurodyn, Munich, Germany 1: 361-366 [3] Cantieni, R. (1983) Dynamic Load Tests on Highway Bridges in Switzerland - 60 Years'

Experience of EMPA. EMPA Report 211 [4] Cantieni, R., Biro, T. (2005) Office Floor Vibrations: Modal Parameter Identification and

Vibration Monitoring. Proc. 6th eurodyn, Paris, France 1, 533-538 [5] Cantieni, R., Brehm, M., Zabel, V., Rauert, T., Hoffmeister, B. (2008) Ambient Testing and

Model Updating of a Bridge for High-Speed Trains. Proc. 26th IMAC, Orlando, Florida [6] Brehm, M., Zabel, V., Cantieni, R. (2009) Modellanpassung einer Eisenbahnbrcke fr den

Hochgeschwindigkeitsverkehr. VDI-Berichte 2063, 403-418, VDI Verlag GmbH, Dsseldorf [7] Cantieni, R. (2009) Modal Analysis of a River Exploitation Power House with and without the

Turbine/Generator Units Being in Operation. Proc. 3rd IOMAC, Portonovo (Ancona), 73-80. [8] Cantieni, R., Pelayo, F., Lpez-Aenlle, M., Fernndez-Canteli, A. (2011) Operational Modal

Analysis of Two Wind-Turbines with Foundation Problems. Proc. 4th IOMAC, Istanbul [9] Cantieni, R. (2011) Traffic Excited Vibrations Acting on Pedestrians Using a Highway Bridge.

Proc. 4th IOMAC, Istanbul [10] Cantieni, R., Rosenquist, M.O. (2011) Experimentelle Modalanalyse einer Strassenbrcke im

Rahmen einer Belastungsanalyse. Proc. DACH-Tagung "Erdbeben und Baudynamik", Hannover [11] Cantieni, R. (2013) Cable-Stayed Footbridge Investigation Into Superstructure and Cable

Dynamics. Proc. 31st IMAC, Garden Grove, California

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http://www.rcidynamics.ch/

1. INTRODUCTION2. steel plate2.1. Topic2.2. Steel plate (2001)2.3. Ambient Excitation?2.4. Test results2.5. Specials: How can we check whether our measurements are good or bad?2.6. What can we learn?

3. short-to-medium-span highway bridge3.1. Topic3.2. A110 bridge (2001, [2])3.3. Ambient Excitation?3.4. Test results3.5. Specials: Minimum number of sensors required?3.6. Specials: What could the fundamental frequency of my bridge be?3.7. What can we learn?

4. Office Floor4.1. Topics4.2. Mainau Office Building (2004, [4])4.3. Ambient Excitation?4.4. Test results4.5. Specials: Minimum number of references required?4.6. What can we learn?

5. Medium-Span Railway bridge5.1. Topic5.2. Erfttal Bridge (2007, [5])5.3. Ambient excitation?5.4. Test results5.5. What can we learn?

6. Power house Global6.1. Topic6.2. Eglisau Power House (2008, [7])6.3. Ambient excitation?6.4. Test results6.5. What can we learn?

7. power house local7.1. Topic7.2. Eglisau Power House (2008, [7])7.3. Ambient excitation?7.4. Test results7.5. What can we learn?

8. machine foundation8.1. Topic8.2. Gijn Fan Foundation (2008)8.3. Ambient excitation?8.4. Test results8.5. What can we learn?

9. Bell tower9.1. Topic9.2. San Luzi Bell Tower (2004, 2009, 2011, 2012)9.3. Ambient excitation?9.4. Test results9.5. What can we learn?

10. Further examples11. CONCLUSIONS

EXPERIMENTAL MODAL ANALYSIS UNDER AMBIENT...

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