Biomedical Engineering Reference
In-Depth Information
Analysis shows that the solution of Eq. (4.109) subject to the initial
conditions of (4.105) is characterized by the limiting relations
max
)
|
x(t)
|→
0
,
max
)
|
c
x
˙
+
kx(t)
|→
ma
(4.111)
t
∈
[0
,
∞
t
∈
[0
,
∞
and
c
2
/(mk)
→∞
if and only if
k
→∞
. Therefore, the viscoelastic model
of attachment of the body to the base can be approximated by the rigid
model if the stiffness and damping coefficients are sufficiently large and, in
addition, if the characteristic time of damping (
m/c
) is much less than the
period of natural undamped vibrations of a body on a spring (2
π
√
m/k
).
4.2 OPTIMAL SHOCK ISOLATION
FOR THREE-COMPONENT STRUCTURES
4.2.1
Introduction
When modeling the dynamics of various moving structures that involve
shock-isolated objects, it is often possible to single out three major compo-
nents that could be conventionally called the
base
,the
container
,andthe
object
to be protected. The base is a body that is the recipient of a shock
disturbance. The container is a body that is attached to the base and that
separates the object from the base. The object is attached to the container
by means of a shock isolator, which is a control device that responds to a
shock with a force that acts on the object so as to mitigate the mechanical
loading to the object. To improve the shock isolation effect, the container
can be attached to the base by means of an additional isolator.
In specific systems, the role of the base, the container, and the object
can be played by different bodies and structures. For instance, for an air-
craft one can regard the landing gear carriage as the base, the fuselage as
the container, and the passengers as the objects to be protected. The seat
cushions play the role of isolators between the fuselage and the passengers
and the landing gear shock absorber can be treated as an additional isolator
between the carriage and the fuselage.
For people who use wheelchairs, the goal is to design a reliable system
that attaches a wheelchair to the body of the transport vehicle (e.g., a bus)
and isolates the wheelchair from the shock while keeping the occupant in
the wheelchair so that the injuries are mitigated. In this case, the base is the
bus, the container is the wheelchair, and the object to be protected is the
occupant of the wheelchair.
In modern crashworthy passenger cars, the isolation of occupants from
impacts in a frontal crash is provided not only by the restraint system (seat
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