FUNDAMENTALS OF IMPACT AND SHOCK ISOLATION - Injury Biomechanics and Control: Optimal Protection from Impact - page 32

2.2 SHOCK ISOLATION

In this section, the concept of shock isolation is introduced and a simple
example is given to explain the physical fundamentals and to investigate
the effectiveness of the isolation.

2.2.1 Shock Isolation of an Object on a Moving Base

Often objects are attached to a body that can be subjected to a shock load.
To reduce the level of the shock load transmitted to shock-sensitive objects,
they are attached to the body by means of a medium or structure that allows
the objects to move relative to the body. An aircraft, when landing, has a
nonzero, although small, vertical component of the velocity. Therefore, the
landing gear undergoes a shock load at the instant the undercarriage wheels
touch the runway. The crew and passengers do not feel the full shock
because the landing gear is equipped with shock absorbers that are located
between the undercarriage and the fuselage. An automobile undergoes a
shock load when it is driven over a hole or bump in a road. This shock is
absorbed by the car suspension, which separates the wheels from the car
body. In a crash, an automobile can be subjected to a high shock load that
can cause injuries to the occupants. To mitigate the injuries, automobiles
are equipped with devices such as seat belts and air bags.
Reducing a shock load transmitted to objects from a body subject to the
load by means of media or structures separating the objects from the body
is called shock isolation . The media or structures that provide this reduction
are called shock isolators .
To understand the physical fundamentals of shock isolation, consider a
simple system that consists of two bodies: the base, which is subjected to
a kinematic shock disturbance, and the object to be protected. Both bodies
move along the same straight line. The motion of this system is governed
by the equations

m x ¨ = u, z ¨ = v(t), (2.24)

where x and z are the absolute coordinates of the object and the base
measured along the line of motion relative to a fixed (inertial) reference
frame, m is the mass of the object, u is the force acting on the object, and
v(t) is the acceleration or deceleration pulse applied to the base. The force
u characterizes the interaction between the object and the base.
If the object is rigidly attached to the base, both bodies move with the
same acceleration v(t) ,thatis, x ¨ =¨ z = v(t) , and, hence, u(t) = mv(t) .The

maximum magnitude (peak magnitude) of this force, max t | mv(t) | , may turn