Field Evaluation of Dampers

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CHAPTER 7

Field Evaluation of Dampers

In order to evaluate the effectiveness of fluid dampers for stay-cable vibration

mitigation and to facilitate the design of even more effective and economical systems, it

is important to perform quantitative assessments of damper performance under various

types of excitation. Toward this end, this chapter seeks to evaluate the effectiveness of

passive linear dampers installed on two stays on the Fred Hartman Bridge in Houston,

Texas, by comparing response statistics before and after the damper installation and by

investigating in detail the damper performance in a few selected records corresponding to

different types of excitation.

Fluid dampers, specified to have a linear force-velocity relationship, have been

installed for evaluation on two stays on the Fred Hartman Bridge, and at the time of

writing, data have been collected for more than two years after the damper installation to

evaluate the damper performance. The two stays on which the evaluation dampers have

been installed are indicated on the schematic drawing of the bridge in Figure 7.1 (AS16

and AS23); this figure also indicates the coordinate system used for reporting wind speed

and wind direction. Properties of the two stays on which evaluation dampers have been

installed are given in Table 7.1 along with the damper locations and the specified damper

coefficients.


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previously, the error in the predictions of the universal curve is most significant near the

optimal portion of the curve, and it is evident here that the asymptotic approximate value

differs most significantly from the exact value in mode 1, for which the damper is nearly

optimal. The error near the optimal portion of the curve becomes more significant in the

higher modes, but because the damper is far from optimal in the higher modes for these

stays, the universal curve gives quite good predictions of the damping ratios in the higher

modes. The Sc > 10 criterion discussed previously requires modal damping ratios of

0.53% for Stay AS16 and 0.64% for Stay AS23. It is evident from Figure 7.2 that,

according to the analytical predictions, this criterion is satisfied in the first nine modes for

Stay AS16 and in the first five modes for Stay AS23. Damping values for the stays have

not yet been directly estimated from measurements for comparison with the analytical

predictions, but work is currently in progress and results will be reported in future

publications (Delong Zuo, personal communication).

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

1 2 3 4 5 6 7 8 9 10

Mode Number,i

AS16: numericalAS16: asymptotic

AS23: numerical

AS23: asymptotic

i

Figure 7.2: Predicted Damping vs. Mode Number for Hartman Stays AS16 and AS23


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In order to assess the presence of the damping-induced frequency shifts predicted

by the analytical formulation, the natural frequencies of Stay AS23 before and after the

damper installation were estimated from the peak values of averaged acceleration power

spectra. Five 5-minute records of ambient vibration under low wind speeds were selected

both before and after the damper installation, and each set of five spectra was averaged to

obtain averaged undamped and damped spectra. The damping-induced frequency shift in

each of the identified modes was computed by taking the difference of the damped and

undamped frequencies. These measured frequency shifts were then normalized by the

fundamental frequency of the stay to obtain dimensionless frequency shifts, which are

plotted in Figure 7.3 for the first 12 modes. Also plotted with the measured values are

the dimensionless frequency shifts predicted by numerical solution of the eigenvalue

equation (3.6) (labeled Analytical), and the frequency shift i which would be

induced if the cable were fixed at the damper location (labeled Clamped). It is evident

that the measured values agree quite well with the analytical predictions, and the

frequency shifts are quite significant, especially in the higher modes.

0

0.1

0.2

0.3

0.4

0.5

1 2 3 4 5 6 7 8 9 10 11 12

Mode Number, i

Measured

Analytical

Clamped: i

1o

oii

f

ff

Figure 7.3: Frequency Shift vs. Mode Number: Estimated and Measured Data


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As was mentioned above, when the dimensionless frequency difference i in a

given mode reaches 0.5, new regimes of behavior are observed. In the case of Stay

AS23, the value of i associated with mode 13 is slightly greater than 0.5, and the

analytical formulation for the taut string with linear damper in Chapter 3 indicates that

the damping in this mode is supercritical, so that no oscillatory solution exists for this

mode, but a non-oscillatory decaying solution emerges instead; this behavior is observed

because the damper is located sufficiently near the antinode of mode 13 for Stay AS23.

In modes 14 and higher, the damper is located past the first antinode, and solution of the

eigenvalue equation indicates that the frequency of damped oscillation is less than the

undamped frequency in these modes. Although not presented herein, the frequency shifts

measured in the higher modes agree reasonably well with the analytical predictions.

The clamping ratio ci associated with each mode can be computed by normalizing

the dimensionless frequency shifts plotted in Figure 7.3 by the dimensionless frequency

difference i. The value of the nondimensional damper parameter associated with

each mode can be readily computed from the definition in (3.32) using the stay and

damper properties in Table 7.1. Figure 7.4 shows the resulting plot of versus ci; a

distinct data point is plotted here for each of the first 12 modes, larger values of

corresponding to higher mode numbers. Also plotted with the measured values are the

analytical values determined from numerical solution of (3.6) and the curve

corresponding to the asymptotic approximation in (3.31). The measured values agree

reasonably well with the analytical predictions, and a clear trend of increasing clamping

ratio with mode number is evident. The measured frequency shifts thus confirm that this


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damper, which was optimized for mode 1, is effectively more rigid in the higher modes

and is tending to lock the cable at the damper location in these modes.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

Measured

Analytical

Asymptotic

ci

Figure 7.4: Non-Dimensional Damping Parameter vs. Clamping Ratio

7.2 Global Damper Performance

In order to evaluate the effectiveness of the trial dampers installed on the two

stays, response statistics are compared from data collected before and after the damper

installation. The data presented herein are obtained from queries issued to the database

described earlier. In order to minimize the inclusion of records with noise-corrupted or

saturated data, all queries include a filter that retains only records with skewness with a

magnitude less than 2.0 and kurtosis less than 5.0 (recall that a normal distribution has a

skewness of zero and a kurtosis of 3.0). (A slightly more aggressive skewness filter of

magnitude less than 1.5 was used for the load cell data). While this scheme obviously

might exclude some data records that are of interest, experience has shown this approach


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to be a reasonable method of eliminating problematic data while retaining the majority of

features being sought.

In the figures included herein, representative values of mean wind speed were

computed using the same scheme described previously in Chapter 2. Wind direction is

measured in degrees clockwise from the bridge axis, with zero degrees corresponding to

wind approximately from the North, directly along the bridge axis, as indicated in Figure

7.1. Acceleration data are reported from transducers installed on the stays usually about

6 m vertically above deck level, and for the purposes of this investigation and for the data

reported herein, the accelerations are reported at the transducer location.

The global performance of the dampers installed on stays AS16 and AS23 is

summarized in Figure 7.5 and Figure 7.6, respectively, which illustrate the following

Characterization of oscillations (in-plane) occurring before installation of the

damper as a function of wind speed and direction.

Characterization of oscillations (in-plane) occurring after the installation of the

damper as a function of wind speed and direction.

Measurement of damper force as a function of wind speed and direction.


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Figure 7.5: Stay Vibration and Damper Force Characteristics: Stay AS16


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Figure 7.6: Stay Vibration and Damper Force Characteristics: Stay AS23

Before the damper is installed, both stays show similar characteristics, and

patterns that are consistent with the field observations that were described earlier. A high

density of points is seen near the abscissa, which generally corresponds to vortex-induced

vibration in a variety of modes and low-level buffeting response of the stay under random


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excitations. Both figures clearly indicate the characteristic signature of wind-rain

oscillation as the multiple points over a wide range of wind speeds that are of high

amplitude i.e., root-mean-square (RMS) accelerations greater than 0.5g. One-minute

mean wind speeds at deck level reached 15 m/s before the dampers were installed, and

almost 18 m/s in the period after installation. This latter value corresponds to a one-

minute average wind speed of 27 m/s (60 mi/h) at the top of the tower, recorded during a

thunderstorm. The dependence on wind direction is also clear, with AS16 showing its

peak responses between 90 and 160 degrees, and AS23 over a narrower range between 90

and 135 degrees. The primary goal of a mitigation system is to reduce significantly or

eliminate these large-amplitude events, while respecting the fact that the stays and bridge

form dynamic systems and will always exhibit some level of dynamic response.

The corresponding figures after the installation of the dampers suggest the

following:

Amplitudes are significantly reduced across all recorded wind speeds (up to 18

m/s at deck level) with maximum RMS acceleration amplitudes of around 0.5g.

The dependence on wind direction has been altered significantly, with the

previously preferred range now largely unapparent, and the largest of the

responses now nearer to a 90-degree angle of incidence. The characteristics of

selected records corresponding to these locations will be discussed in more detail

later.

The third pair of figures shows the RMS damper force for the two installed

devices as a function again of wind speed and direction. For stay AS16, the

pattern of forces resembles closely the pre-damper acceleration figures (both in


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terms of wind speed and direction), suggesting that the dampers are being

engaged by the stays to suppress proclivity towards wind-rain vibration.

Relatively high-magnitude forces are also seen in the complementary range of

225 to 270 degrees, which represent wind directions also corresponding to the

declining direction of the stay (but now from the southwest rather than southeast.)

For stay AS23, the behavior is similar, though perhaps not as clear as in the

previous case. Much of the high force data for this stay is now clustered around

an incident angle of 90 degrees, although some up to 110 degrees are evident. An

interesting and unusual cluster of points labeled Record C will be discussed

subsequently. Note that in all the records, the highest amplitude RMS force

recorded is approximately 5.6 kN (1125 lb) a relatively modest level of load.

7.3 Analysis of Individual Records

While comprehensive investigation of all individual data records is challenging

due to the quantity of data, it is instructive and interesting to study some of these specific

records in some detail in order to better understand what the dampers are doing, or trying

to do. After some review of these datasets, three such representative records have been

selected and presented herein. These records are labeled A, B, and C in Figure 7.5 and

Figure 7.6; Records A and B are selected from stay AS16, and record C from stay AS23.

The reasons for the selection, as well as an interpretation of each record is provided

below. Each figure includes a ten-second time history of acceleration and damper force,

as well as a PSD of each over a 10-Hertz range.

Record A (Figure 7.7) represented one of the highest amplitude RMS acceleration

events after the installation of the damper on stay AS16. It corresponded to a wind speed


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of about 3.4 m/s and a wind direction of 60 degrees. The RMS force is moderate: about 2

kN RMS. This record is interpreted as traditional vortex-induced vibration of the stay,

with both acceleration and force presenting strongly single-mode responses at a

frequency of about 6.5 Hz. (This corresponds to the fifth mode of vibration of this

dampedstay. As noted above, the damper has a stiffening effect on the stay system that

is mode dependent; the frequency of the fifth mode of the undamped stay is

approximately 6.2 Hz.) An analysis of the Strouhal relationship for this wind speed and

frequency suggests a Strouhal number consistent with 0.2: the value commonly assumed

for a circular cylinder. Due to the relatively high frequency of the mode, displacement

amplitudes associated with this motion are small even with the peak acceleration of 1g

(about 6 mm at the transducer location.)


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Stay AS16 Acceleration Time History (Record A)

-1.5

-1

-0.5

0

0.5

1

1.5

0 2 4 6 8 10

Time (s)

Acceleration(g)

Stay AS16 Acceleration PSD (Record A)

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.0E+02

0 2 4 6 8 10

Frequency (Hz)

PSDof

Acceleration

Stay AS16 Damper Force Time History (Record A)

-10

-8

-6

-4

-20

2

4

6

8

10

0 2 4 6 8 10

Time (s)

Force

(kN)

Stay AS16 Damper Force PSD (Record A)

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-021.0E-01

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

0 2 4 6 8 10

Frequency (Hz)

PSDofDam

perForce

Figure 7.7: Time History and PSD of Stay Acceleration and Damper Force

(Record A AS16)

Record B (Figure 7.8) represented another of the highest amplitude RMS

acceleration events after the installation of the damper on stay AS16, but corresponded to

a wind speed of about 8.5 m/s and a wind direction of 90 degrees. The RMS force is one

of the largest recorded for this stay: about 4.8 kN RMS. The acceleration and force plots

both clearly contain two main frequency components, one at about 2.6 Hz and the other

at 5.3 Hz, corresponding to the second and fourth modes of the damped stay,

respectively. The force data are dominated by the second-mode contribution. A number

of other modes are evident in both spectra, but note that the log scale tends to exaggerate

their relative contributions. The characteristics of this record suggest that it is a case of

wind-rain vibration that is being suppressed by the damper, and analysis of the rain


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bucket data confirms the presence of moderate rainfall at the time of this record (a

rainfall rate of approximately 25 mm/hr was estimated). Note also the strong asymmetric

appearance of the acceleration record (and to a lesser extent the force record.) Indeed

this acceleration record has a mean of zero and is in fact not asymmetric; the addition of

the appropriately phased second and fourth modes gives this appearance. It should be

noted, however, that the two components conspire to produce peak accelerations of about

1g and a peak load in the damper of a little over 9 kN (2000 lb). These values are

certainly higher than what one would estimate assuming mono-frequency response.

Consideration of the peaks as well as RMS values should generally be undertaken for this

reason. The damper is certainly able to effectively control/reduce the large-amplitude

behavior observed before the installation, and again through the provision of modest

levels of force.


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Stay AS16 Acceleration Time History (Record B)

-1.5

-1

-0.5

0

0.5

1

1.5

0 2 4 6 8 10

Time (s)

Acceleration(g)

Stay AS16 Acceleration PSD (Record B)

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.0E+02

0 2 4 6 8 10

Frequency (Hz)

PSDof

Acceleration

Stay AS16 Damper Force Time History (Record B)

-10

-8

-6

-4

-20

2

4

6

8

10

0 2 4 6 8 10

Time (s)

Force

(kN)

Stay AS16 Damper Force PSD (Record B)

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-021.0E-01

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

0 2 4 6 8 10

Frequency (Hz)

PSDofDam

perForce


(Record B AS16)

Record C (Figure 7.9) represented the highest amplitude RMS force recorded to

date on stay AS23, even though the acceleration measured on the stay was small. This

corresponded to a wind speed of about 10 m/s and a wind direction of 60 degrees. The

RMS force is the largest recorded for this stay: about 5.7 kN RMS. This record is very

unusual and interesting for a number of reasons. Note that the acceleration amplitude is

relatively small about 0.25g and clearly contains a broad range of frequency

components. The peak force magnitude, however, is close to 8 kN (1800 lb) and is

dominated (strongly) by the fundamental mode of the stay at 0.66 Hz. Again, the multi-

frequency contributions plotted at log scale exaggerate the higher mode contributions; the

most significant higher mode contribution is more than two orders of magnitude lower


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than that of the fundamental mode. This is believed to be an example of deck-stay

interaction that the damper is responding to suppress. First, it is unusual to see such a

strong component of force at the fundamental mode of the stay, as preceding data have

suggested. Ozkan et al. (2001) discuss a situation where oscillation of a stay was clearly

preceded and presumably precipitated by oscillation of the deck of the structure in the

fifth vertical mode of vibration. As discussed therein, the analysis suggested that in

that case stay AS24 had a fundamental frequency very close to the third symmetric

vertical mode of the deck, which evidently drove the stay in its fundamental mode. A

vertical deck frequency was also identified at 0.67 Hz, which in this case is quite

likely driving (or attempting to drive) stay AS23 in its fundamental mode. Unfortunately,

the deck accelerometers were non-functional at the time this record was made, so this

hypothesis cannot be confirmed in this case by reference to deck data. Again, the damper

seemed to perform well under these circumstances.


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Stay AS23 Acceleration Time History (Record C)

-1.5

-1

-0.5

0

0.5

1

1.5

0 2 4 6 8 10

Time (s)

Acceleration(g)

Stay AS23 Acceleration PSD (Record C)

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.0E+02

0 2 4 6 8 10

Frequency (Hz)

PSDof

Acceleration

Stay AS23 Damper Force Time History (Record C)

-10

-8

-6

-4

-20

2

4

6

8

10

0 2 4 6 8 10

Time (s)

Force

(kN)

Stay AS23 -- Record C

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

0 2 4 6 8 10

Frequency (Hz)

PSDofDam

perForce


(Record C AS23)

7.4 General Remarks

The preceding section demonstrates that under a wide range of field parameters

that the damper solution appears to provide a reasonable and acceptable solution to the

stay cable vibration phenomenon. Despite these promising results, a few comments and

cautions are in order.

The ranges of wind speeds evaluated, even over a three-year period, are limited.

It has been suggested that high-wind-speed phenomena such as galloping might

occur in inclined stay cables, and that a damper solution would be incapable of

providing sufficient capacity to suppress such phenomena. While we have not

Field Evaluation of Dampers

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