Biomedical Engineering Reference
In-Depth Information
bodies. The sled moves along a horizontal straight line relative to a fixed
(inertial) reference frame and the dummy moves relative to the sled along
the same line. The function
v(t)
represents the crash deceleration pulse of
the sled, the coordinate
x
measures the displacement of the dummy rela-
tive to the sled, and
u
is the absolute acceleration of the dummy due to
the force applied to the dummy by the restraint system. The acceleration
u
characterizes the force transmitted to the dummy, since it is equal to this
force divided by the mass of the dummy. Sometimes the variable
u
will
be referred to as the force. The relation of Eq. (3.185) simulates the elastic
and dissipative properties of the seat belts.
In the sled tests, the class
W
occurring in the statements of Problems 3.7
and 3.8 normally characterizes a set of disturbances that are representative
of the test, taking into account the inevitable uncertainties in the identifi-
cation of the precise deceleration pulse. Often, the class of representative
disturbances involves a “corridor” or “envelope” similar to that of Fig. 3.12,
in which these disturbances must lie, that is,
W
={
v(t)
:
v
−
(t)
≤
v(t)
≤
v
+
(t), t
∈
[0
,T
]
}
,
(3.189)
where
v
−
(t)
and
v
+
(t)
are prescribed functions that define the lower and
upper bounds of the corridor and
T
is a fixed time. In addition, the velocity
of the sled should change by a certain value during the crash pulse time
T
.
In the case of a kinematic disturbance, this condition has the form
T
V
=
v(t) dt,
(3.190)
0
where
V
is a specified positive quantity. Usually, the quantity
V
is pre-
scribed with an allowance for an error in the measurement of the velocity
of the sled,
V
−
≤
V
≤
V
+
,
(3.191)
where the interval [
V
−
,V
+
] characterizes the uncertainty in the measure-
ment of the velocity decrease. Since
V
is defined as the integral of
v
,the
inequalities of Eq. (3.191) impose additional constraints on the deceler-
ation pulse time history. Therefore, the total class to which the allowed
deceleration pulses must belong is defined by
T
W
={
v(t)
:
v
−
(t)
≤
v(t)
≤
v
+
(t), V
−
≤
v(t) dt
≤
V
+
}
.
(3.192)
0
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