FUNDAMENTALS OF IMPACT AND SHOCK ISOLATION - Injury Biomechanics and Control: Optimal Protection from Impact - page 21

will be classified as a shock disturbance if, respectively,
∞

∞

| F (t) | dt < ∞ or | w (t) | dt < ∞ , (2.9)

t 0 t 0

where w (t) r (t) is the acceleration of the point of application of the

kinematic disturbance and t 0 is the initial time of the disturbance. The
relations of Eq. (2.9) hold for finite-duration disturbances for which F (t) ≡
0or w (t) ≡

= ¨

0for t > t 0 + τ ,where τ is the duration of the disturbance.
The relations of Eq. (2.9) formally permit an infinite time of action for
the disturbance, but the “result” of this action, measured by the respective
integrals, is finite.
Consider some important examples of shock disturbances in which the
force F (t) or acceleration w (t) do not change the line of action but they
can change in direction along this line. In this case, one can characterize
the disturbance by the scalar functions F(t) or w(t) , the projections of the
corresponding vector functions onto the unit vector of the line of action.
In the examples, dynamic disturbances will be considered. For kinematic
disturbances, simply change F to w in the appropriate relationships.

Example 2.1 Rectangular Pulse

Consider a rectangular pulse

A

≤ t ≤ T,
0if t > T,

if 0

F(t) = (1)

where A and T are specified constants. The function F(t) is plotted in
Fig. 2.2 for A > 0 . The integral involved in Eq. (2.9) for function (1) is
∞

T

| F(t) | dt = | F(t) | dt =| A | T. (2)

0 0

F

A

0 t

T

FIGURE 2.2 Rectangular pulse.