13th World Conference on Earthquake Engineering
Vancouver, B.C., Canada
August 1-6, 2004
Paper No. 643

STUDY ON BASED-ISOLATION OF WOODEN HOUSESBY HEAT HARDENING PORYURETHANE RUBBER
Ryota MURAYAMA 1, Toshiyuki KANAKUBO2, Akira YASOJIMA3,
Nao MINATO4, Tomoki FURUTA5 and Takashi TSUJIMOTO6SUMMARY
This paper investigates effectiveness and mechanical characteristics of heat hardening polyurethane
rubber (PUR) for viscoelastic dampers in based-isolated and vibration controlled wooden houses. Since
PUR shows low stiffness and high damping compared with the conventional viscoelastic materials, it issuitable for based-isolated device for small-scale structures such as wooden houses. In addition, PUR is
not expensive so it is possible to build up based-isolated system in low cost. From the results of sinusoidal
loading tests of PUR, the mechanical characteristics are estimated. PUR has frequency dependency, strain
dependency, temperature dependency, and axial pressure dependency. Especially in them, axial pressure
dependency is important. Because there is the problem of axial pressure dependency that equivalent
stiffness of PUR increases with the increment of pressure, when it is used as based-isolation device. The
Kelvin-Voigt model is build up based on the results of test. In this study, laminated PUR bearing is
proposed to control axial pressure. From the results of vibration test for the laminated PUR bearing, lowequivalent stiffness and high equivalent viscous damping factor is observed even if axial pressure exists.
The results of seismic response analysis show the effectiveness of laminated PUR bearings for basedisolated structures.
INTRODUCTION
The purpose of a based-isolated structure is not transfer1ing energy of an earthquake to an upper structure.
A structure is separated from the ground by the isolator and absorbs energy of earthquake with dampers.
Therefore, based-isolation devices are required for vertical strength, low stiffness, and high damping.
However, the usual based-isolation devices for wooden house are difficult for realization of these points.
Because weight of wooden house is small, it is difficult to lengthen a natural period. And the cost for
1

Master program student, University of Tsukuba, Japan
Dr.E., Assistant Prof., Institute of Engineering Mechanics and Systems, University of Tsukuba, Japan
3
ME, Doctor program student, University of Tsukuba, Japan
4
Master program student, Tokyo Institute of Technology, Japan
5
Dr.E., Division of Isolation and Control Devices, Bando Chemical Industries, Japan
6
Director, Bando Chemical Industries, Japan2

based-isolation devices becomes high. Since PUR shows low stiffness and high damping compared withthe conventional viscoelastic dampers, it is suitable for based-isolated device for small-scale structures
such as wooden houses. In addition, PUR is not expensive so it is possible to build up based-isolated
system in low cost. It is inserted between base of house and ground sill. The role of isolator and damper isavailable by PUR. In this study, based-isolation device using PUR is proposed.
VISCOELASTIC MATERIAL
Fundamental Mechanical Characteristic
Viscoelastic material is the high polymer material having the character of viscosity and elasticity.
Viscocity means that material shows reactive force by viscous resistance proportional to speed. Elasticity
shows the force proportional to deformation. Recently, in a field of architecture, it is spreading widely as
viscoelastic damper aiming for energy absorption in vibration control structure. Viscoelastic material canabsorb vibration energy by resistance with histerisis loop (Fig.1). This damper performs high energy
absorption from small amplitude such as vibrations of wind and traffic to large earthquake. For thatreason, it is effective in vibration control of structure.
Fundamental mechanical characteristic of PUR is represented by equivalent stiffness (Keq), equivalent
damping coefficient (Ceq), and equivalent damping factor (heq). Resisting force of viscoelastic material is
proportional to cross section area (As) and shear thickness (d). Fundamental mechanical characteristic of
PUR is able to be estimated by small-sized test piece. Therefore, it can be estimated shape factor.
τG'G'' γ0γ

0γ

K eq =

C eq =

As
G'
d
ηK eq

ω
1 ∆W η
heq = ・=
4π W 2

Loss factor η = tan δ =G"G'

γ 0 : Maximum shear strain∆W : Absorbed energy

Fig.1 Histerisis loop of viscoelastic material
Mechanical characteristic can be divided into viscosity and elasticity. In case of sin wave, shear stress (τ)
can be represented as τ = G' γ 0 sin( ωt ) + G" γ 0 cos( ωt ) with storage modulus (G’) and loss modulus (G”).
In this numerical expression, the first term of the equation shows elasticity, and second shows viscosity.
SIN WAVE VIBRATION TESTS OF PUR
Outline of Experiment
It is known that fundamental mechanical characteristics of viscoelastic
materials are influenced by temperature, frequency, and share strain. In
this study, PUR is developed for based-isolation device of wooden
house. So, it is necessary to investigate fundamental mechanicalcharacteristics and dependencies. Fig.2 shows test piece (section:

50*50mm, thickness: 5, 10, 20, 40mm). When it use for wooden
house, several tens of PUR (section: 100*100mm) set between
base and ground sill. Therefore, in this test, four test pieces aretested as one set.

Fig.2 Test piece

Loading system is shown in Fig.3 and Fig.4. For adding axial pressure equally, four test pieces are fixed
on the ground sill, and weights are set on them. In addition, two supports are set to the both sides ofweights in order to restrict rotation. Both sides of load cell are pin joint. The number of cycles is at least
10 times. Parameters of loading are frequency (0.2~5Hz), shear strain (20~300%), temperature (-20~60deg.), and axial pressure (0~1.0N/mm2). Observed values of load and displacement are averaged in 2 to 10
cycles. Measurement terms are load, displacement, temperature. In the case of the test with a weight, shear
stress and strain are calculated using thickness and sectional area of test piece after setting a weight.

Weights
Load cell
Ground sill
Test pieces

Fig.3 Loading system

Fig.4 Experimental condition

Test Results
Histerisis loop
Fig.5 shows histerisis loop (thickness: 5mm, frequency: 1Hz, axial force: 0 or 10kN, temperature: 20deg ofCelsius.). Strain-softening characteristic is observed.
1000
5000

Load(N)

Load(N)

500

Frequency:1Hz
Axial Pressure:0kN
Temperature:20℃

0Frequency:1Hz
Axial Pressure:10kN
Temperature:20℃

0

-500
-5000
-1000
-200

-100
0
100
Shear Strain(%)

200

-200

-100
0
100
Shear Strain(%)

200

Fig.5 Histerisis loop
Frequency, shear strain dependency
The relationship between storage modulus (G’) and frequency, loss modulus (G”) and frequency are
shown in Fig.6. From Fig.6, it is confirmed G’ and G” increase as same as the increase in frequency, anddecrease with the increase in shear strain. Equivalent damping factor (heq) is not influenced by frequency
and shear strain.
Temperature dependency
The relationship between storage modulus (G’) and temperature, loss modulus (G”) and temperature areshown in Fig.7. G’ and G” are influenced by temperature. Ones for 0 deg. increase as 1.5 times for 20
deg. and ones for 40 deg. decrease as 0.6 times. These values are not so large compared to ordinaryviscoelastic material. In addition, equivalent damping factor (heq) show almost constant value in spite of
temperature change.
0.15
29%
64%
109%
149%

0.1

43%
87%
132%
165%

G"(N/mm2)

G'(N/mm 2)

0.15

0.05

1

0

2
3
4
5
Frequency(Hz)0.1

Thickness ：5mm
Axial Force ：0kN
Temperature：20℃

0.05

6

1

0

2
3
4
5
Frequency(Hz)6

Fig.6 Frequency, shear strain dependency
0.3

0.3
0.5Hz
2Hz

0.2

G"(N/mm 2)

G'(N/mm 2)

0.2Hz
1Hz
5Hz

0.1

0

-20

0
20
40
Temperature( ℃)

0.2

0.1

0

60

Thickness ：5mm
Shear Strain ：50%
Axial Force ：0kN

-20

0
20
40
Temperature( ℃)60

Fig.7 Temperature dependency
Thickness dependency
Resistance force of viscoelastic material is in proportional to shape factor (As /d). For each thickness PUR,
the relationship between storage modulus (G’) and frequency, loss modulus (G”) and frequency are
shown in Fig.8. Each thickness PUR show almost same value. Similar result is obtained in case of igh
axial pressure as well. Therefore, thickness dependency can be estimated by shape factor.
0.1

G"(N/mm 2)

G'(N/mm 2)

0.1

0.05
40mm
20mm
10mm
5mm
0

1

2
3
4
5
Frequency(Hz)6

Axial Force : 0kN
Shear Strain : 60%
Temperature : 20 ℃
0.05

0

1

2
3
4
5
Frequency(Hz)6

Fig.8 Thickness dependency
Axial pressure dependency
The relationship between storage modulus (G’) and axial pressure, loss modulus (G”) and axial pressure
are shown in Fig.9. From Fig.9, it is confirmed that G’ and G” increase as axial pressure also increases.
Equivalent damping factor (heq) is not influenced by axial pressure.

0.4

Temperature : 20 ℃
Shear Strain : 60%

0.5Hz
2Hz
G"(N/mm 2)

G'(N/mm 2)

0.3

0.3
0.2Hz
1Hz
5Hz

0.2

0.2

0.1

0.1

0

0.2 0.4 0.6 0.8 1
Axial Pressure (N/mm 2)

0.2 0.4 0.6 0.8 1
Axial Pressure (N/mm 2)0

Fig.9 Axial pressure dependency
MODELING
Method of Modeling
It has been reported in the previous studies that each dependency (frequency, share strain, andtemperature) of viscoelastic material can be treated independently. So, storage modulus( G'ref ) and loss
modulus( G"ref ) is estimated based on the test results for shear stain of 60%, axial pressure of 0 N/mm2,
and temperature of 20 deg. Celsius. Each dependenciy is introduced as shift factor. Therefore, storage
modulus (G’) and loss modulus (G”) are show in Eq.(1) and Eq.(2). Kelvin-Voigt model is used torepresent constitutive law of PUR defined by G' and G" .
G ' ( f , γ , T , σ ) = G ' ref ( f ) ⋅ ρ G ',γ (γ ) ⋅ λG ',T (T ) ⋅ κ G ',σ (σ )(1)G" ( f , γ , T , σ ) = G" ref ( f ) ⋅ ρ G",γ (γ ) ⋅ λG ",T (T ) ⋅ κ G ",σ (σ )(2)ρ : shift factor for shear strain dependency
λ : shift factor for temperature dependency
κ : shift factor for axial pressure dependency

In addition, time moment frequency (ft ) is derived from Eq.(3) [1]. Therefore, time history response
analysis by equivalent stiffness (Keq) and equivalent damping coefficient (Ceq) can be carried out.
ft =

1
2π

n

∑ v t − v t − j∆t

j =1

2

2

n

(3)

∑ x t − j∆t − x t
2

2

j =1

v t , xt : velocity and displacement in time moment of t.

Determination of Shift Factors
Fig.10 shows the relationships between frequency and storage modulus (G’) for the loading case of shear
strain of 60% as the base of the modeling. Indicated formula is obtained by least-square method. Fig.11
shows shift factor of each dependency. Shift factors are decided according to regression analysis by leastsquares method. Although there is a little variation, each dependency can be expressed by indicatedformulas. The same estimation is carried out for loss modulus (G”). Therefore, model of storage modulus(G’) and loss modulus (G”) considering each dependency of PUR are shown in Eq.(4) and Eq.(5).
⎛ 65.6 ⎞G ' = 0.0578 f 0.411 ⋅ e −0.590γ ⋅ (0.628 + 2.53 σ ) ⋅ ⎜⎟⎝ 45.9 + T ⎠

1.46

(4)

⎛ 101 ⎞G" = 0.0513 f 0.252 ⋅ e −0.486γ ⋅ (0.631 + 2.45 σ ) ⋅ ⎜⎟⎝ 81.7 + T ⎠

2.80

(5)

f : frequency(Hz), γ : share strain(%), σ : axial pressure(N/mm2), T : temperature(degree)
0.15

G'ref (N/mm2)

Frequency
DependencyG'ref
0.1

0.05

0.0392 f 0.411
Experiment

0

1

2
3
4
5
Frequency f (Hz)6

Fig.10 Base storage modulus (G’)
5
St rain Dpendency ρG',γ4

Experiment

G'/G'T=20℃

G'/G'γ = 60%

1.5

1.47 e-0.590γ

15
T emperat ure
DependencyλG',T

0.5

3
1.46

65.6
( 45.9+T)

2
1

G'/G'σ = 0, 0.2N/mm2

2

Axial Pressure
DependencyκG',σ4

0.628+2.53 √σ

3
2
1

Experiment

Experiment
0

100
200
Shear St rain γ (%)

300

0

-20

0
20 40 60
T emperatureT (℃)

0.5
1
Axial prssureσ (N/mm2)0

Fig.11 Shift factor of each dependency
Adaptability of Model
Comparisons between test results and model are shown in Fig.12. Modeled histerisis loops show a good
agreement with test results. Fig.13 shows comparison between result of randomly dynamic loading
response test and analytical result using proposed model. The response analysis is carried out using singlemass model in which the upper part of structure is assumed to be rigid body. The based-isolation layer isrepresented by proposed Kelvin-Voigt model. The analysis is done by direct integration using Newmark βmethod. Input wave is time history data which is acceleration obtained by vibration table in the response
test Result of experiment and analysis show a good correspondence.
1000

-1000
-200

Axial Force:0kN
Temperature:20℃

0

-500
Model
Experiment

-100
0
100
Shear st rain (%)

200

Model
Experiment

-1000
-200

-100
0
100
Shear st rain (%)

Fig.12 Comparing Histerisis loop

200

Response Accelation (gal)

500

0

-500

1000

1000 Frequency:1Hz
Load (N)Load (N)500

Frequency:1Hz
Axial Force:0kN
Temperature:20℃

500
0
-500

Experiment
Model

-1000
13

14

15
16
T ime (s)17Fig.13 Comparing response

18

LAMINATED PUR BEARING
Outline of Experiment
From the results of vibration test, mechanical characteristics of PUR are strongly influenced by axialpressure. Considering PUR as isolated devices, it is important that equivalent stiffness should becontrolled at low level in spite of the increment of axial pressure. The shape factor decreases as much as
PUR becomes thick. And this leads the decrement of the stiffness of PUR. For the purpose of proposing
low stiffness bearing device, laminated PUR bearing is proposed. Because thin PUR has small influenceof axial pressure, laminated PUR can keep suitable shape factor and low stiffness even if axial pressure
exists. In this study, vibration test for the laminated PUR bearing is conducted to compare withmechanical characteristics of PUR.
Test pieces are laminated PUR (section: 50*50mm, thickness: 9mm for 1 layer) and steel plate (diameter:
50mm, thickness: 1mm) with 4 layers. It is covered with rubber tube (thickness: 2mm, inner diameter:
49mm, width: 40mm). The test pieces are shown in Fig.14．Experimental equipment is the same as thecase of sin wave vibration tests of PUR. Parameters of input sin wave are frequency (0.2, 0.5, 1.0, 2.0, 5.0
Hz), shear strain, and axial force (0, 2, 5, 10kN).

Test piece

Inside of the test piece
Fig.14 Laminated PUR

Test Results
Fig.15 shows histerisis loop obtained by loading test. Fig.16 and Fig.17 show equivalent stiffness andequivalent damping factor. The results of 40mm PUR are compared with laminated PUR. Equivalent
stiffness of laminated PUR is sufficiently small comparing with 40mm PUR. And laminated PUR has
high damping as same as 40mm PUR.
Modeling
From the result of loading test, differences in mechanical characteristics of laminated PUR and 40mm
400 Frequency 1Hz

4000 Frequency 1Hz

200

2000

Axial Load 10kN

Load(N)

Load(N)

Axial Load 0kN

0

0

-200

-2000

-400

-4000
-100

0
Shear Strain(%)

100-200 -100 0 100 200
Shear Strain(%)

Fig.15 Histerisis loop of laminated PUR

40

20
10
0

50
100
Shear Strain(%)

Frequency 1Hz
Axial Force 10kN

300

200

100

150

0

100
200
300
Shear Strain(%)

80
Frequency 1Hz
Axial Force 0kN

60
40
20

0

50
100
Shear Strain(%)

Equivalent Damping Factor(%)

Equivalent Damping Factor(%)

Fig.16 Equivalent stiffness80
Frequency 1Hz
Axial Force 10kN

60
40
20

150

0

100
200
300
Shear Strain(%)

Fig.17 Equivalent Damping Factor

Model
Experiment

30
20
10
0

50
100
Shear Strain(%)

150

80
60

Frequency 1Hz
Axial Force 0kN

40
20

0

50
100
Shear Strain(%)

Equivalent Stiffness(N/mm)

40600
Frequency 2Hz
Axial Force 0kN

150

500

Frequency 2Hz
Axial Force 10kN

400
300
200
100
0

Equivalent Damping Factor(%)

Equivalent Stiffness(N/mm)

50

Equivalent Damping Factor(%)

Result of Analysis
Maximum responses by Bcj-L2 andEl Centro NS are shown in Fig.19.
Effect of based-isolation can be
expected that maximum response
acceleration decreases. When thenumber of laminating is 30,
response acceleration decreases 1/2– 1/3 time in comparison with nonisolated houses. In addition, shear
strain of laminated bearing is
restrained within 100%. Therefore,
it is considered that the mostsuitable number of laminating isabout 30 layers.

Frequency 1Hz
Axial Force 0kN

30

SEISMIC RESPONSEANALYSIS
Method of Analysis
A target structure for seismic
response analysis is the two-story
wooden house which weight is 35tf.
Laminated PUR bearings (section:
100*100mm) are set between thebase and ground sill. The number ofbearings is assumed to 35. Analysis
variavle is number of laminating.
Analysis model is single-massmodel in which the upper part ofstructure is assumed to be rigid
body. The based-isolation layer isrepresented using proposed KelvinVoigt model. Response analysis istime history response analysis bydirect integration using Newmark βmethod. Input waves are simulated
wave of Building Center of Japan(Bcj-L1, Bcj-L2) and El Centro NS.

40mmP UR
Laminat ed P UR

Equivalent Stiffness(N/mm)

50
Equivalent Stiffness(N/mm)

PUR are depended on shape factor.
Therefore, model for laminated PUR
is expressed as same as model of
PUR. Fig.18 shows comparisons
between test results and model’svalue. Since model’s value canrepresent experiment value well. So,
the same model can be used forlaminated PUR bearing.

50 100 150 200 250
Shear Strain(%)

80
60

Frequency 1Hz
Axial Force 10kN

40
20

0

50 100 150 200 250
Shear Strain(%)

Fig.18 Comparison between test results and model’s valuebcj-L2

400

200

0

600

Max Response Acc(gal)

Max Response Dis(cm)

600

20

500

10
20
30
Number of Laminating

Natural Period （s）
0.6 0.8 1.0
1.2
1.4

400
300
200
100
0

10
20
30
Number of Laminatingbcj-L210

10

Elcent ro NS

40

Natural Period （s）
0.6 0.8 1.0
1.2
1.4

0

40

Max Response Dis(cm)

Max Response Acc(gal)Natural Period （s）
0.6 0.8 1.0
1.2
1.4

10
20
30
Number of Laminating

40

Natural Period （s）
0.6 0.8 1.0
1.2
1.4
Elcent ro NS

8
6
4
2
0

10
20
30
Number of Laminating40

Fig.19 Maximum response
CONCLUSIONS
Vibration test and seismic response analysis which is conducted to investigate the fundamental
mechanical characteristic of PUR and effectiveness for based-isolated structures are carried out. The
followings are concluded.
1. PUR has frequency dependency, strain dependency, temperature dependency, and axial pressure
dependency. Especially, axial pressure dependency is bigger. The equivalent stiffness increases asaxial pressure also increases.
2. Equivalent stiffness of laminated PUR is sufficiently small comparing with 40mm PUR. Laminated
PUR has high damping as same as 40mm PUR.
3. Mechanical characteristic of PUR can be expressed by shift factors which involve each dependency.
Characteristics of laminated PUR is also represented by same model of PUR
4. From the seismic response analysis of laminated PUR bearing, laminated PUR bearings are effective
for based-isolated structures.
5. It is considered that the most suitable number of laminating is about 30 layers.
REFERENCES
1.

Yi-Hua HUANG, Takashi KATO, Akira WADA, Mamoru IWATA, Toru TAKEUCHI, and Kiyoshi
OKUMA : The dynamic Mechanical model of viscoelastic dampers relying on the frequency andtemperature, J. Struct. Constr. Eng., AIJ No.516, P91-98, Feb., 1999