Biomedical Engineering Reference
In-Depth Information
achieve a reduction in load, as compared with the case of equipment rigidly
connected to the foundation, it is necessary that
u
0
<f
0
. Substitute
F(t)
of Eq. (2.67) and
u(t)
of Eq. (2.68) into Eq. (2.65) and solve the resulting
equation subject to zero initial conditions
x(
0
)
=
0and
x(
0
)
˙
=
0 to obtain
⎧
⎨
2
m
f
0
u
0
t
2
1
−
if 0
≤
t
≤
τ,
tτ
f
0
m
τ
2
2
u
0
2
m
t
2
x(t)
=
−
−
if
τ<t
≤
τ
1
,
(2.69)
⎩
f
0
u
0
1
f
0
τ
2
2
m
−
if
t > τ
1
,
where
f
0
u
0
τ.
τ
1
=
(2.70)
Due to the inequality
u
0
<f
0
resulting from the requirement that the iso-
lation must reduce the load transmitted to the foundation,
τ
1
> τ
. Equation
(2.69) is an analogue of Eqs. (2.43) and (2.54) for the motion of an object
to be protected relative to a moving base.
The effectiveness of the shock isolation can be evaluated in terms of the
shock isolator stroke (the maximum displacement of the equipment relative
to the base),
R
∗
, and the displacement of the free (completely isolated from
the foundation) equipment for the shock pulse time,
P
∗
. The quantity
R
∗
is an analogue of the rattlespace and
P
∗
is an analogue of the quantities
P
b
and
P
c
in the relations of Eqs. (2.39) and (2.64) used to evaluate the
effectiveness of the isolation of an object from a moving base subjected to
an impact load.
The displacement
P
∗
is determined by
f
0
)τ
2
2
m
(mg
+
P
∗
=
.
(2.71)
According to Eq. (2.69), the shock isolator stroke is expressed by
f
0
f
0
1
.
P
∗
f
0
mg
R
∗
=
−
(2.72)
u
0
+
The effectiveness of the isolation can be measured by the ratio
f
0
mg
+
E
=
u
0
.
(2.73)
mg
+
Search WWH ::
Custom Search