Biomedical Engineering Reference
In-Depth Information
F
(
t
)
Equipment
m
x
u
FIGURE 2.8
Equipment on a fixed foundation.
where
x
is the coordinate of the mass measured vertically downward from
some fixed point and
g
is the acceleration due to gravity. If the equipment
is rigidly attached to the base, then
x
=
0 and, hence, the force transmitted
to the foundation is
−
u
=
F
+
mg.
(2.66)
Assume that the impact force acts downward and its time history has the
form of a rectangular pulse, that is,
f
0
≤
≤
if 0
t
τ,
F(t)
=
(2.67)
0if
t
>
τ,
where
f
0
is the force magnitude
(f
0
>
0
)
and
τ
is the pulse duration.
In this case, with reference to Eq. (2.66), the peak force transmitted to
the foundation to which the equipment is rigidly attached is
f
0
+
mg
.To
reduce this load, it is necessary to isolate the equipment from the foundation
and to allow the equipment to move relative to the foundation in response
to the shock pulse of Eq. (2.67). Assume that the force
u
acting between
the equipment and the foundation has the form
−
u
0
mg
−
if 0
≤
t
≤
τ
1
,
u(t)
=
(2.68)
−
mg
if
t > τ
1
,
where
u
0
is a positive quantity and
τ
1
is the time at which the equipment
excited by the shock pulse comes to a complete stop. In this case, the
peak magnitude of the force transmitted to the foundation is
mg
u
0
.To
+
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