INTRODUCTION - Injury Biomechanics and Control: Optimal Protection from Impact - page 5

m 1

m 2

F

FIGURE 1.2 Two-body model with a spring-and-dashpot element.

the spring-and-dashpot element imitates the elastic and viscous properties
of the vertebral column. The isolator produces the control force F between
the base and the body m 2 . It is required to find an optimal control force
that minimizes the maximum magnitude of the displacement of body m 2
relative to the base, provided that the magnitude of the force developed
in the spring-and-dashpot element does not exceed a prescribed value. The
shock disturbance is specified as the time history of the absolute acceleration
of the base. The presence of impulse components in the control force is
established and proved. An algorithm for constructing the optimal control
is described. A general concept for the limiting performance analysis is
introduced for systems that involve three components: a base, a container
in which the object is placed, and the object. Shock isolators separate the
container from the base and the object from the container. This model can be
used to represent vehicles equipped with shock isolation systems to reduce
occupant injuries in a crash.
In Chapter 5, a simple model of a crashworthy helicopter seat is con-
sidered. The seat may be equipped with one or two active isolators. One
isolator (a cushion) separates the lower torso of an occupant from the seat
pan, and the other separates the seat pan from the helicopter's airframe. The
isolators are optimized to protect an occupant from severe spinal injury
for a hard landing of the helicopter. A two-degree-of-freedom model is
used to simulate the response of the vertebral column to a vertical impact
load. To construct the optimal controls and to evaluate the minimum dis-
placement of the lower torso relative to the seat pan, the technique of
Chapter 4 is employed. To validate the results obtained on the basis of the
two-degree-of-freedom spinal injury model, a MADYMO multibody model