Biomedical Engineering Reference
In-Depth Information
out to be unacceptably high for the object. For the peak magnitude of the
force acting on the object to be reduced, this object must move with another
acceleration time history,
w(t)
, such that max
t
|
mw(t)
|
<
max
t
|
mv(t)
|
.In
this case, the object will necessarily move relative to the base, and, hence,
to reduce the shock load transmitted from the base to the object, a space for
the relative motion should be allowed. This space is sometimes referred to
as the
rattlespace
. The rattlespace is measured by the difference between
the maximum and minimum coordinates of the object relative to the base,
R
=
max
t
[
x(t)
−
z(t)
]
−
min
t
[
x(t)
−
z(t)
]
.
(2.25)
For a preliminary investigation of the effectiveness of shock isolation,
we assume that the object and the base move with the same velocity
V
until the base hits an obstacle at a time instant
t
0. This impact results
in the uniform deceleration of the base until it comes to a complete stop.
In this case, the variables of Eq. (2.24) should be subjected to the initial
conditions
=
x(
0
)
=
0
,
z(
0
)
=
0
,
x(
0
)
=
V,
z(
0
)
=
V
(2.26)
and the shock pulse
v(t)
is specified as follows:
⎧
⎨
V
a
,
−
a
if 0
≤
t
≤
v(t)
=
(2.27)
if
t >
V
⎩
0
a
,
where
a
is the deceleration magnitude
(a >
0
)
.
The absolute motion of the base is given by
⎧
⎨
⎧
⎨
V
a
,
at
2
2
V
a
,
−
≤
V
at
if
t
Vt
−
if
t
≤
z
˙
=
z
=
(2.28)
if
t >
V
V
2
2
a
⎩
⎩
if
t
>
V
0
a
,
a
.
In accordance with these relations, the deceleration time of the base is
V/a
and the deceleration path is
V
2
2
a
.
P
b
=
(2.29)
If the object is rigidly attached to the base, the peak magnitude of the force
transmitted to the object is
F
1
=
ma
.
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