Civil Engineering Reference
In-Depth Information
As far as the eigenfrequencies of the table is concerned, it is a direct function of
the dimensions of the table and its design features. The most common tables are
between 1 m x 1 m to 3 m x 3 m in size. The largest tables are 6 m x 6 m large
(CEA/Saclay in France, Berkley in the USA). A few exceptional tables can reach 15
m x 15 m (Tadotsu in Japan). Plans are underway to allow coupling between several
large-size tables. The tables themselves are generally made of steel, though some are
made of pre-stressed concrete. As they are quite heavy, they are problematic as far
as the mass or the maximum acceleration are concerned. In order to improve
performance, tables can be made of aluminum or composite materials.
With small shaking tables that use small servo-valves, the maximum frequencies
due to the responses of servo-valves are about 100 to 150 Hz. With other
installations requiring high-outflow servo-valves, the maximum frequencies are
about 50 to 100 Hz. To improve the frequency efficiency with some big
installations, it is possible to use several smaller servo-valves mounted in parallel,
themselves used as drivers to operate the racks allowing high outflows.
The resonance frequency of the oil column is due to the compressibility of the
compressed oil inside the jack chambers. Although oil has a very high bulk
modulus, the stiffness of the oil column is low enough for the frequency of the oil
column to be within the relevant frequency range of the table.
2
The stiffness of the oil column is given by the formula
K = 4 S B/V
where:
S is the section of the jack piston;
B is the oil bulk modulus (= 1.4 x 10
9
N/m²); and
V is the whole volume of oil enclosed in the jack.
1/ 2
The oil column frequency is then given by
F = 1/2ʌ. K/ M
M
.
t
s
For large shaking tables, the frequency ranges from 8 to 20 Hz depending on the
load (for example, the frequency of the oil column of the AZALEE table in the
vertical direction with a 50 ton model is about 20 Hz).
Another limitation is due to the stiffness of the table. Though it is reinforced and
therefore quite stiff, the table is supported either by vertical hinged jacks or by truss
rods or sliding rails. Such equipment has a finite stiffness which influences the
behavior of the model and which should be taken into account for the calculation of
the eigenfrequencies of the model. In many cases, a 6 Hz frequency model will have,
once laid on the table, a bending frequency of 5 to 5.5 Hz.
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