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

Thank you for your kind attention