ABSTRACT A vibration isolation system using spring units and visco ...

ABSTRACT
(Revised English Version)
A vibration isolation system using spring units and visco-elastic dampers can reduce vibration and
structure borne noise in a building near subway or other traffic facilities effectively. For applying
this system in Japan, it is necessary to confirm the seismic safety. So an experimental and
analytical study was done.
At first static loading tests of the spring units and dynamic loading tests of a visco-elastic damper
were carried out. Then analytical models for the springs and visco-elastic dampers were
developed. At the next stage shaking table tests with the model of a vibration isolated building
were performed in order to examine the vibration characteristics and behaviours of the structure.
Finally a four story vibration isolated building supported by such a system was designed with the
confirmation of the seismic safety of the building by analysis based on the proposed model.
KEYWORDS
vibration isolation system, helical steel spring, visco-elastic damper, loading test, shaking table
test, response analysis.
1. INTRODUCTION
Recently many buildings have been constructed near subways or other traffic facilities in inner city
areas of Japan where vibration or structure borne noise reduces the quality of life of the people
living here. To avoid this problem, it is useful to adopt vibration isolation systems using spring units
and visco-elastic dampers. For this purpose, an experimental and analytical study has been done
including the design of a four story building with consideration of its seismic safety.

2. VIBRATION ISOLATION SYSTEM
2.1 Details of the system
Helical steel springs are used to support the weight of the building providing a low vertical natural
frequency of the spring supported building, so that the higher frequency parts of the traffic
vibrations can be isolated to a high degree. The visco-elastic dampers react in all three
dimensions. They can, therefore, be placed near to the corners of the building.
Both, springs and dampers, are concentrated in several locations where the number of spring units
and dampers is controlled by the load distribution of the upper structure.
The system has the following characteristics:
1) With helical spring support of the building its natural frequencies, both in vertical and horizontal
direction, can be set quite low, so that vibration and structure borne noise from subways or
other traffic is highly reduced.
2) Since visco-elastic dampers react three dimensionally, it is needless to arrange dampers for
vertical and horizontal direction independently, and it is, therefore, easy to concentrate the
devices in the corners.
Fig. 1 Sectional plan of the building Fig. 2 Arrangement of devices in the building

2.2 Composition of the system
2.2.1 Helical steel spring elements
Several helical steel springs are used as a spring unit. Usually a spring unit, consisting of the
springs and a top and bottom plate, can resist only compression forces. But in this special system,
springs can resist compression and tension force because both ends of the springs are fixed to the
end plates (see Fig. 3).
Fig. 3 Spring unit Fig. 4 Damper
2.2.2 Visco-elastic dampers
Visco-elastic dampers consist of three parts as shown in Fig. 4.
(1) Lower cylindrical vessel
(2) Visco-elastic liquid in the vessel
(3) Cylindrical piston submerged in the visco-elastic liquid.
The cylindrical piston can move in the visco-elastic liquid three-dimensionally relative to the
movement of the lower vessel transferring vibration energy in this way into heat.
3. DYNAMIC TEST OF THE DEVICES
Several dynamic tests of the spring units and the visco-elastic dampers were done.
3.1 Dynamic test of the characteristics of the spring unit
3.1.1 Outline of the test
The spring unit contains seven helical steel springs fixed to the end plates. The natural frequency
in the vertical direction of the spring supported system is 2.5 Hz.
The test pattern is
(1) Horizontal loading test at different displacements in vertical direction.
(2) Vertical loading test at some displacements in horizontal direction.

3.1.2 Cyclic horizontal loading test
(1) Loading
At first the spring unit is deformed vertically by - 20 mm, - 10 mm (tension), 5 mm, 15 mm, 40 mm
(compression). Then the unit is pushed in two horizontal directions in a right angle by a cyclic load
of a hydraulic jack.
(2) Displacements
The horizontal displacement is ± 10 mm in the first cycle, ± 20 mm in the second cycle, ± 30 mm in
the third cycle and ± 42 mm in the forth cycle.
(3) Results
Fig. 5 shows the relation between horizontal load and displacement.
Fig. 6 shows the relation between horizontal spring rate and vertical displacement.
According to Fig. 6, the horizontal spring rate increases with increasing vertical displacements. The
results are the same in both horizontal directions.
Fig. 5 Horizontal load-displacement line Fig. 6 Relation between horizontal spring rate
and vertical displacement
3.1.3 Cyclic vertical loading test
(1) Loading
At first the spring unit is deformed horizontally by 0 mm, 30 mm, 42 mm. Then the unit is
dynamically loaded in vertical direction cyclically by a hydraulic jack.
(2) Displacements
At first the spring unit is compressed statically by 40 mm. Then it is vertically loaded by ± 20 mm in
the first cycle, ± 30 mm in the second cycle, ± 40 mm in the third cycle and ± 50 mm in the fourth
cycle.

(3) Results
Fig. 7 shows the relation between vertical load and displacement.
Fig. 8 shows the relation between vertical stiffness and horizontal displacement.
According to Fig. 8 vertical stiffness increases at increasing horizontal displacements.
Fig. 7 Vertical load displacement line Fig. 8 Vertical stiffness versus horizontal displacement
3.2 Test of the characteristics of the visco-elastic damper
3.2.1 Outline of the test
The vertical and horizontal characteristics of the visco-elastic damper were found in a test with
random noise excitation and tests with sinusoidal force excitation at several frequencies.
3.2.2 Vibration test in vertical and horizontal direction
(1) Vibration
Vibrations were excited by random noise or sinusoidal loads. The frequency range of the random
noise was 0 to 5 Hz and 3 to 50 Hz. The amplitude range was very small. The amplitude range of
the vertical sinusoidal excitation was 5 ~ 45 mm at 1 Hz, 5 ~ 15 mm at 2 Hz and 2 ~ 12 mm at
5 Hz. The amplitude range of the horizontal sinusoidal excitation was 5 ~ 30 mm at 1 Hz,
5 ~ 15 mm at 1,5 Hz and 2 ~ 15 mm at 3 Hz.
�� Results of random noise excitation
Fig. 9 Displacement dependency
of damping resistance

(2) Result
According to the tests, the damping coefficient decreases and the stiffness increases with
increasing frequency.
Fig. 9 shows the displacement dependency of the damping coefficient. The horizontal damping
coefficient decreased down to 87 % compared to that at random noise excitation when the
amplitude was 30 mm. The vertical damping coefficient decreased down to 60 % compared to that
at random noise excitation when the amplitude was 45 mm.
4. SEISMIC RESPONSE ANALYSIS OF THE VIBRATION ISOLATED BUILDING
4.1 Analysis model
The analysis model is shown in Fig. 10
(1) The upper parts of the building were assumed as concentrated masses connected by springs.
(2) The ground floor was assumed as a solid slab.
(3) The spring elements and visco-elastic dampers were put under the columns of the ground floor.
(4) The analysis model was designed as a three dimensional model.
The data for the analysis are shown in Table 1.
Fig. 10 Analysis model of the building
4.1.1 Modelling of the springs
The spring coefficients of the spring depend on the deformation of the spring. The model of the
spring (shown in Fig. 11) was, therefore, composed of a vertical spring and a multi spring element
for the horizontal shear direction. Both elements were given restoration characteristics gained from
the experiments. The response calculation was done step by step with the tangential stiffness at
each step.

4.1.2 Modelling of the damper
The damping coefficients have a displacement dependency according to the experiments. These
dynamic characteristics of the damper are introduced into a four parameter model as shown in
Fig 12,
Fig. 11 Isolation spring element Fig. 12 4 parameter model Table 2 Parameters of the 4 parameter model
where the damping coefficients and the damper stiffnesses are taken into account according to the
experiments for every frequency. According to Fig. 9 the damping coefficients were reduced to
87 % in the horizontal direction and to 60 % in the vertical direction. The parameters of the
4 parameter model are shown in Table 2.
4.2 The procedure of the response analysis
With the help of a three dimensional frequency response analysis program and a three
dimensional time history response analysis program the response analysis was done as follows.
(1) The spring rates of the spring unit were assumed to be linear. In this way the three dimensional
frequency response analysis program was run. Next, the three dimensional time history response
analysis program was run. Then the similarity of the two wave forms gained from the two analysis
was compared.
(2) The spring was modeled as a combination of a vertical spring element and a multi spring
element for the horizontal shear direction. The damper was modeled as a four parameter model as
shown in Fig. 12. Then the three dimensional frequency response analysis program was run.
4.3 Earthquake records used
Earthquake records used in this analysis were modified from those of El Centro, Taft and
Hachinohe Earthquakes. The strength levels of the earthquake records were 50 kine for the
horizontal NS and EW direction vectors.

4.4 Results
The acceleration time histories of X and Y directions for the roof floor resulting from the three
dimensional frequency response analysis and the three dimensional time history response analysis
based on the EW wave of El Centro in X direction are shown in Fig. 13. Both time histories are
very similar in wave form and maximum acceleration.
(a) Frequency response analysis (b) Time history response analysis
Fig. 13 Acceleration response (RFX,Y-direction)
(a) Frequency response analysis (b) Time history response analysis Table 3 Maximum response
Fig. 14 Transfer function (RF X-direction)
The transfer functions of the two response analyses are shown in Fig. 14. Both are very similar
below 10 Hz, but above 10 Hz the response of the time history analysis is lower than that of the
frequency response analysis.
The detailed analysis results are shown in Table 3.

5. SHAKING TABLE TEST OF THE ISOLATED BUILDING MODEL
5.1 Shaking table test
5.1.1 Model
The model was designed to have the same natural frequency and the same damping ratio as the
real building. The isolation system was composed of six springs and four dampers. The
accelerations at the top and bottom of the frame, and the relative displacement between the
bottom of the frame and the top of the shaking table were measured. Fig. 15 shows the model and
measurement points.
5.1.2 Loading
(1) Sinusoidal sweep excitation
The model was shaken by a sinusoidal sweep wave in the direction of the longer side (X), the
shorter side (Y) and the vertical direction (Z). The acceleration was 20 gal and the range of
frequency was 0.3 Hz - 10.0 Hz.
(2) Seismic excitation
Taft wave, El Centro wave and Hachinohe wave were used for the input of the shaking table. For
each seismic wave the model was shaken in Y direction only, Y and Z directions combined and all
three directions.
5.2 Analytical method
The analytical method of the shaking table test was the same as the one explained already above.
The analysis model is shown in Fig. 16. The upper structure was assumed to be a shear beam
element. The weight of the model was concentrated in two separate masses at the top and the
bottom. The material properties of the analysis model were based on the results of a random noise
test without the isolation system.
4-parameter model
Longitudinal cross section Lateral cross section
Fig. 15 Specimen Fig. 16 Analysis model

5.3 Comparison of the shaking table test and the simulation
5.3.1 Vibration properties
The natural frequencies are in both cases very similar. The amplitude of the simulation is a little
smaller than that of the shaking table test.
5.3.2 Seismic excitation
The Y direction response time history for the three dimensional Taft wave excitation is shown in
Fig. 17. The amplitudes of the simulation are smaller than those of the table test. But acceleration
and displacement are very similar. The similarity confirms the accuracy of the model.
The maximum response acceleration ratio of the model at the maximum acceleration of the
shaking table is shown in Table 4. In the cases of El Centro wave and Hachinohe wave the results
are for one dimensional excitation. In the case of Taft wave those are for one, two and three
dimensional excitation.
The response acceleration ratio increased only a little bit horizontally, but vertically more for the
three dimensional excitation than for the two dimensional one.
Fig. 17 Y-direction time history response (for TAFT 3-D) Table 4 Maximum acceleration response amplitude
6. CONCLUSION
A four story building was designed and certified for the maximum response. From our
investigations the following can be concluded.
1) In the vibration isolated building supported by springs and visco-elastic dampers vibration and
structure borne noise levels caused by traffic will be effectively reduced.
2) The characteristics of the dampers can be modelled properly by a 4 parameter model
respectively those of the springs by a multi-direction shear spring.
3) The 3 dimensional analysis of the models shows a good coincidence with the shaking table test,
so that it can be used for analyzing a real building with a vibration isolation system.