Biomedical Engineering Reference
In-Depth Information
The absolute motion of the base is given by
⎧
⎨
⎩
⎧
⎨
⎩
at
2
2
V
a
,
V
a
,
at
if
t
≤
if
t
≤
z
=
z
=
(2.36)
if
t >
V
V
2
2
a
if
t >
V
V
a
,
Vt
−
a
.
The base accelerates during the time
V/a
and then moves with constant
velocity
V
. The path traveled by the base during this time (the acceleration
path) is expressed by Eq. (2.29).
Assume that the object is isolated from the base and is accelerated by a
constant force
mw
during the time
w/V
to the velocity
V
coinciding with
the final velocity of the base. For the magnitude of the force transmitted to
the object to be reduced, it is necessary that
w<a
. The acceleration pulse
of the object has the form
⎧
⎨
⎩
V
w
,
w
if 0
≤
t
≤
u(t)
m
=
(2.37)
0if
t >
V
w
,
and its absolute motion is defined by
⎧
⎨
⎧
⎨
wt
2
2
V
w
,
V
w
,
wt
if
t
≤
if
t
≤
x
˙
=
x
=
(2.38)
⎩
⎩
if
t >
V
V
2
2
w
if
t
>
V
V
w
,
Vt
−
w
.
The acceleration path of the object is expressed by Eq. (2.32). The rat-
tlespace in the case under consideration is equal to the difference of the
acceleration paths of the object and the base and is given by Eq. (2.33).
Solve Eq. (2.33) for the ratio
a/w
to obtain
a
w
=
R
P
b
.
1
+
(2.39)
The ratio
a/w
is equal to the ratio of the peak magnitude of the force
transmitted to the object rigidly attached to the base to that of the force
transmitted to the isolated object
(a/w
F
1
/F
2
)
and, hence, characterizes
the effectiveness of the shock isolation. It is apparent from Eq. (2.39) that
the larger
R/P
b
is, the greater the effectiveness. As
R/P
b
→
=
0, the ratio
a/w
tends to unity and, hence, the isolation becomes ineffective. Remember
that
P
b
is the deceleration or acceleration path of the base. Hence, the
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