Page 113 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

100 Transient Vibration Chap. 4

-)
Ç /max

Figure 4.3-4.

Example 4.3-3
For a man in a seated position, as when driving an automobile, the single-DOF model
of Fig. 4.3-5 is often assumed for forensic studies. From extensive biomechanical
tests, the spinal stiffness of 81,000 N/m = 458 Ib/in.^ is assumed for the spring k
supporting the body mass W/g. By assuming mg = 160 lb, this results in a static
deflection of 3^, = 160/458 = 0.35 in. Let us assume that in hitting an obstacle, the
driver not restrained by a seat belt is thrown upward and drops 3.0 in. in free fall onto
an unpadded stationary seat. Determine the g acceleration transmitted by his spinal
cord.
Solution: The result for this problem is simply obtained from Eq. (d) of Example 4.3-2 as

f T x X 3
+ 1 = - ■ + 1 = -4.26
V 0.3 '.35

4.4 PULSE EXCITATION AND RISE TIME

In this section, we consider the time response of the undamped spring-mass system
to three different excitations shov/n in Fig. 4.4-1. For each of these force excita­
tions, the time response must be considered in two parts, t < and t >

Rise time. The input can be considered to be the sum of two ramp
functions, as shown in Fig. 4.4-2. For the first ramp function, the terms of the
^See Ref. [5].