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5WCSCMFifth World Conference on Structural Control and Monitoring12 - 14 JULY 2010
Influence of Vibration Methods, Structural Components and Excitation Amplitude on Modal Parameters of Low-rise Building
T.H. Le1), S. Nakata2), A. Yoshida1), S. Kiriyama2), S. Naito3) and Y. Tamura1)
1) Tokyo Polytechnic University, Japan2) Asahi Kasei Homes Corporation Co., Ltd., Japan
3) Taku Structural Design Co., Ltd., Japan
Introduction Stiffness evaluation is essential for low-rise buildings where structural components can strongly influence on dynamic properties due to sensitiveness on distribution of mass, stiffness and damping. Stiffness evaluation can be investigated indirectly via evaluation of changes of modal parameters.
Up to now, investigations on influence of the structural components and their stiffness contribution on the low-rise buildings are rare
Evaluation of influence of excitation amplitudes on the damping and natural frequency has been done somewhere [ex., Tamura and Suganuma, 1996]
Objectives
Investigate influences of structural components, levels of excitation amplitudes and type of vibration tests on modal parameters (Natural frequencies and damping) of the experimental low-rise building Structural components
ALC walls, sealing joints, interior cover plate, interior separate wall, window
Vibration testsAmbient vibration; forced sweep vibration and free decay vibration tests
Amplitude levelsFrom small to medium and large amplitudes
Experimental low-rise building
‚a‚Q' | ‚R‚a‚Q' | ‚Q
3,39
9
3,660 2,440
‚a‚P' | ‚Q ‚a‚P' | ‚Q
Fig. 1 Experimental low-rise building and accelerometer arrangement
2,440
3660
‚r ‚a ‚P
‚r‚a
‚Q‚r
‚a‚Q
‚r‚a
‚Q‚r
‚a‚Q
‚r‚a
‚Q‚r
‚a‚Q
Steel bracing
Z
X
ALC walls
Sealing joint
2F
1F
Shaker’s location
2,440
3660
‚r ‚a ‚P
‚r‚a
‚Q‚r
‚a‚Q
‚r‚a
‚Q‚r
‚a‚Q
‚r‚a
‚Q‚r
‚a‚Q
2F
1F
PU4-X
PU5-X
PU1-X
PU2-XPU3-X
PU4-
Y
PU6-X
PU6-
Y
Vibration tests have been implemented in the experimental one-storey building
Using 08 accelerometers (03 at 1st Floor, 05 at 2nd Floor)Sampling rate 100Hz
Structural components & erection cases
Case D1 Case D2
Steel frameALC walls(X directions)Sealing
Case D3
Case D4
Interior cover plate
Case D5 Case D6
Interior separateWall (X direction)
Window and exterior wall (Y direction)
Sealing
Fig. 2 Images of structural components and erection cases
Structural components
Structural installation
Erectioncases
Combination of structural components Weight (kN)
Steel frame only D1 87.2
ALC exterior walls (X dir.) D2 + 88.1
Sealing between ALC walls D3 + + 88.1
Interior cover plate D4 + + + 89.7
Interior separate wall D5 + + + + 90.7
Window and exterior wall (Y dir.) D6 + + + + + 92.5
Erection cases and combination of structural components
Vibration tests & test sequences Three types of vibration tests have been carried outAmbient vibration tests
Using microtremor Linear sweep tests
Shaker installed at 2nd floor for linear sweep testsChangeable frequency from 2Hz to 6Hz, with sweep rate of 0.01Hz/s
Free decay testsStop moving mass of the shaker at resonant state
Sequence of vibration tests
Sequence No. Vibration tests Amplitude levels Index
1 Ambient test - Ambient (At First)
2 Sweep test Small Sweep (Small)
3 Free decay test Small Free decay (Small)
4 Sweep test Medium Sweep (Medium)
5 Free decay test Medium Free decay (Medium)
6 Sweep test Large Sweep (Large)
7 Free decay test Large Free decay (Large)
8 Ambient test - Ambient (At Last)
Sequence of vibration tests at each test case (D1-D6)
0 10 20 30 40 50 60
-0.1
-0.05
0
0.05
0.1
0.15
Time (s)
Acc
e. (m
/s2 )
CH04 - PU4X - 2F
CH04
Free decay (medium amplitude)
PU4-X
0 50 100 150 200 250 300-0.01
-0.005
0
0.005
0.01
Time (s)
Acc
e. (m
/s2 )
CH04 - PU4X - 2F
CH04
Ambient (5-minute record)
PU4-X
0 500 1000 1500 2000 2500 3000 3500-8
-6
-4
-2
0
2
4x 10-3
Time (s)
Acce
. (m
/s2 )
CH04 - PU4X - 2F
CH04
Ambient (1-hour record) PU4-X
0 100 200 300 400 500 600 700-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Time (s)
Acce
. (m
/s2 )
CH04 - PU4X - 2F
CH04
Sweep (small amplitude)
PU4-X
0 100 200 300 400 500 600 700
-0.1
-0.05
0
0.05
0.1
0.15
Time (s)
Acce
. (m
/s2 )
CH04 - PU4X - 2F
CH04
Sweep (medium amplitude)
PU4-X
0 10 20 30 40 50 60 70-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Time (s)
Acc
e. (m
/s2 )
CH04 - PU4X - 2F
CH04
Free decay (small amplitude)
PU4-X
Response accelerations at case D1
Fig. 3 Accelerations based on vibration tests and amplitude levels of case D1
Am
bien
t dat
a Fr
ee d
ecay
dat
a Sw
eep
data
Max amplitude: 8cm/s2 Max amplitude: 13cm/s2
Max amplitude: 6cm/s2 Max amplitude: 10cm/s2
Max amplitude: 0.9cm/s2 Max amplitude: 4cm/s2
Natural frequency estimation
Ambient vibration data Power Spectral Density Function (PSD)
[Bendat and Piersol, 1993] Frequency Domain Decomposition (FDD)
[Brincker et al. 2001] Free decay vibration data Power Spectral Density Function (PSD)
[Bendat and Piersol, 1993] Sweep vibration data Frequency Response Function (FRF)
[He and Fu, 2001; Gloth and Sinapius, 2004; Marchitti, 2006; Orlando et al., 2008]
Natural frequency at case D1
0 1 2 3 4 5 6 7 8 9 1010-10
10-8
10-6
10-4
10-2
100
Frequency (Hz)
Nor
mal
ized
spe
ctra
l val
ues
Ambient - case D1
Sepctral value 1Spectral value 2Spectral value 3Spectral value 4
3.59Hz 3.77Hz
6.47Hz
Ambient (At First)
0 1 2 3 4 5 6 7 8 9 1010-10
10-8
10-6
10-4
10-2
100
Frequency (Hz)
Nor
mal
ized
spe
ctra
l val
ues
Ambient - case D1
Sepctral value 1Spectral value 2Spectral value 3Spectral value 4
5.05Hz
3.67HzAmbient (At Last)
0 1 2 3 4 5 6 7 8 9 1010-12
10-10
10-8
10-6
10-4
10-2
Frequency (Hz)
PSD
(m2 /s
)
Free decay - case D1
PU4-X3.69Hz
Free decay (Small)
0 1 2 3 4 5 6 7 8 9 1010-15
10-10
10-5
100
Frequency (Hz)
PSD
(m2 /s
)
Free decay - case D1
PU4-X3.67Hz
Free decay (Medium)
0 1 2 3 4 5 6 7 8 9 1010-4
10-3
10-2
10-1
100
101
Frequency (Hz)
FRF
Sweep (small amplitude)
Single blockBlock overlapping (0%)Block overlapping (50%)
3.69Hz
0 1 2 3 4 5 6 7 8 9 1010-4
10-3
10-2
10-1
100
101
Frequency (Hz)
FRF
Sweep (medium amplitude)
Single blockBlock overlapping (0%)Block overlapping (50%)
3.67HzSweep (Small ) Sweep (Medium )
Fig. 4 Natural frequency estimation based on vibration tests, amplitude levels of caseD1
Spec
tral v
alue
s of
Am
bien
t dat
a PS
D o
fFr
ee d
ecay
dat
a FR
F of
Sw
eep
data
Max amplitude: 8cm/s2 Max amplitude: 13cm/s2
Max amplitude: 6cm/s2 Max amplitude: 10cm/s2
Max amplitude: 0.9cm/s2 Max amplitude: 1.4cm/s2
First natural frequencies D1÷D6First natural frequency in X-direction at small amplitudes
D1 D2 D3 D4 D5 D63.6
3.8
4
4.2
4.4
4.6
4.8
5First natural frequency (X-direction)
Erection cases
Freq
uenc
y (H
z)
AmbientSweepFree decay
Ambient (At Last)
Sweep (Small)
Free decay (Small)
Fig. 5 Influence of vibration tests and erection cases on natural frequency (X direction)
Cases D1 D2 D3 D4 D5 D6Ambient (At First) 3.77Hz 3.76Hz 4.2Hz 4.5Hz 4.64Hz 4.67Hz
Change (%) * -0.3 +11 +19 +23 +24Change (%) ** -0.3 +12 +8 +4 +1
Sweep (Small) 3.69Hz 3.74Hz 4.05Hz 4.33Hz 4.33Hz 4.25HzChange (%) * +1 +10 +17 +17 +15
Change (%) ** +1 +8 +7 0 -2Free decay (Small) 3.69Hz 3.74Hz 4.11Hz 4.47Hz 4.55Hz 4.25Hz
Change (%) * +1 +11 +21 +23 +15Change (%) ** +1 +10 +9 +2 -7
*: Change of frequency compared to D1 ** : Change of frequency compared to previous erection case
Structural components significantly change the natural frequency of low-rise building
Structural components increases the global stiffness of low-rise building
Natural frequency reduces from ambient data to free decay data and sweep data
First natural frequencies D1÷D6First natural frequency in Y-direction at small amplitude
D1 D2 D3 D4 D5 D65
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8First natural frequency (Y-direction)
Erection cases
Freq
uenc
y (H
z)
AmbientSweepFree decay
Ambient (At Last)Sweep (Small)
Free decay (Small)
Fig. 6 Influence of vibration tests and erection cases on natural frequency (Y direction)
Cases D1 D2 D3 D4 D5 D6Ambient (At Last) 5.05Hz 5.03Hz 5.05Hz 5.21Hz 5.16Hz 5.77Hz
Change (%) * -0.4 0 +3 +2 +14Change (%) ** -0.5 +1 +4 -1 +16
Sweep (Small) 5.05Hz 5.01Hz 5.03Hz 5.18Hz 5.16Hz 5.72HzChange (%) * -1 -0.4 +3 +2 +13
Change (%) ** -1 +0.4 +3 0 +11Free decay (Small) 5.05Hz 5.03Hz 5.03Hz 5.18Hz 5.16Hz 5.67Hz
Change (%) * -0.4 -0.4 +3 +2 +12Change (%) ** -0.4 0 +3 0 +10
*: Change of frequency compared to D1 ** : Change of frequency compared to previous erection case
Fig. 7 Influence of excitation amplitudes on natural frequency (X direction)
D1 D2 D3 D4 D5 D63.4
3.6
3.8
4
4.2
4.4First natural frequency (Sweep)
Erection cases
Freq
uenc
y (H
z)
Small amplitudeMedium amplitudeLarge amplitude
Small amplitude
Medium amplitude
Large amplitude
D1 D2 D3 D4 D5 D63.6
3.8
4
4.2
4.4
4.6First natural frequency (Free decay)
Erection cases
Freq
uenc
y (H
z)
Small amplitudeMedium amplitudeLarge amplitude
Small amplitude
Medium amplitude
Large amplitude
Influence of excitation amplitudes on frequency[1]Fi
rst n
atur
al fr
eque
ncy
of
swee
p da
taFi
rst n
atur
al fr
eque
ncy
of
free
deca
y da
ta
Natural frequency reduces with increase of excitation amplitude
Influence of excitation amplitudes on frequency[2]
0 2 4 6 8 10 12 143.5
4
4.5
5
5.5
6Amplitude-depandant frequency (erection cases)
Standard deviation amplitude (cm/s2)
Freq
uenc
y (H
z)
D1D2D3D4D5D6
0 2 4 6 8 10 12 143.5
4
4.5
5
5.5
6Amplitude-dependant frequency (vibration tests)
Standard deviation amplitude (cm/s2)
Freq
uenc
y (H
z)
Ambient (At first)Sweep (Small)Sweep (Medium)Sweep (Large)Free decay (Small)Free decay (Medium)Free decay (Large)Ambient (At last)
Fig. 8 Dependence of natural frequency on excitation amplitudes
Dep
ende
nce
on e
xcita
tion
ampl
itude
s bas
ed o
n er
ectio
n ca
ses
Dep
ende
nce
on e
xcita
tion
ampl
itude
s bas
ed o
n vi
brat
ion
test
s
Damping estimation
Ambient vibration data Random Decrement Technique (RDT)
[Zhang and Tamura, 2003; Tamura et al., 2005] Free decay vibration data Logarithmic Decrement Technique (LDT)
[He and Fu, 2001] Sweep vibration data Half Power Bandwidth Technique (HPB) from FRF
[Bendat and Piersol, 1993; He and Fu, 2001]
Damping ratios D1÷D6
D1 D2 D3 D4 D5 D60
0.5
1
1.5
2
2.5Damping (Ambient & Free decay)
Erection cases
Dam
ping
ratio
s (%
)
Ambient (At first)Free decay (Small amplitude)
D1 D2 D3 D4 D5 D60
0.5
1
1.5
2
2.5
3
3.5Damping (Free decay)
Erection cases
Dam
ping
ratio
s (%
)
Small amplitudeMedium amplitudeLarge amplitude
Ambient (At First)
Free decay (Small)
Fig. 9 Influence of vibration tests and excitation amplitudes on damping ratios
Medium amplitude
Small amplitude
Dam
ping
ratio
s of a
mbi
ent
and
free
deca
y da
ta
Dam
ping
ratio
s of f
ree
deca
y da
ta b
ased
on
exci
tatio
n am
plitu
des
Large amplitude
Damping ratios increase with erection cases from D1 to D6
Damping ratios reduce from free decay data to ambient data
Damping ratios increase with increase of excitation amplitudes
2 4 6 8 10 12 14 16 18 20 220
1
2
3
4
5
6Amplitude dependant damping
Amplitude (gal)
Dam
ping
ratio
(%)
Small amplitude 1Small amplitude 2Medium amplitude 1Medium amplitude 2Large amplitude 1Large amplitude 2
Amplitude (cm/s2)
0 2 4 6 8 10 12 14 16 180
1
2
3
4Amplitude dependant damping
Amplitude (gal)
Dam
ping
ratio
(%)
Small amplitude 1Small amplitude 2Medium amplitude 1Medium amplitude 2Large amplitude 1Large amplitude 2
Amplitude (cm/s2)
Amplitude-dependant damping
Fig. 10 Amplitude-dependant damping (from free decay data)
Am
plitu
de-d
epen
dant
da
mpi
ng o
f fre
e de
cay
data
(Cas
e D
3)
Am
plitu
de-d
epen
dant
da
mpi
ng o
f fre
e de
cay
data
(Cas
e D
4)
Conclusion
Structural components significantly influence to the natural frequency and damping ratios of the experimental low-rise building. To some extent, structural components improve the global stiffness of low-rise building
Natural frequencies reduce gradually from the ambient data to the free decay data and sweep data, whereas the damping ratios increase from the ambient data to the free decay data
Excitation amplitudes also significantly influence on the natural frequency and damping ratios. Concretely, the large amplitudes reduce the natural frequency, but increase the damping
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