Page 295 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

272 BIOMECHANICS OF THE HUMAN BODY

prediction is obtained with the addition of a second mass, m , on the seat platform to represent the
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mass of the torso and legs that does not move relative to the seat (i.e., to the base of the model). The
apparent mass measured on 60 subjects (24 men, 24 women, and 12 children) can be well repre-
sented by this model when the legs are supported to move in phase with the seat, and the data are
normalized for the different weights of individuals using the value of apparent mass recorded at
0.5 Hz (Fairley and Griffin, 1989). A comparison of the observed values for the magnitude, and
phase, of the normalized apparent mass (continuous lines) and the predicted values (dashed lines) is
shown in Fig. 11.7. To obtain this agreement, the natural angular frequency of the model is 31.4 rad/s
(i.e., f = 5 Hz), and the damping ratio is 0.475. These values differ considerably from those of the
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DRI model (see above), reflecting the stimulus magnitude dependent, nonlinear response of the
human body to vibration.

FIGURE 11.7 Comparison between predicted and observed apparent mass.
The mean, normalized apparent masses of 60 subjects, ±1 standard deviation, are
shown by the continuous lines, and the predictions of a single-degree-of-freedom,
lumped parameter biodynamic model by the dashed line. (Fairley et al., 1989.)

Whole-Body Impedance, Apparent Mass, and Transmissibility for Vertical (z-direction)
Vibration. A model has been developed to predict idealized values for the input impedance, apparent
mass, and transmissibility of the seated human body when subjected to vertical vibration. The
model, shown in Fig. 11.8, comprises elements forming three of the models sketched in Fig. 11.6
(ISO 5982, 2001). It contains elements similar to those used to predict apparent mass on the left-
hand side of the diagram with, in addition, two basic models in series to the right of the diagram
(i.e., one on top of the other), in order to represent “head” motion (i.e., motion of mass m ). The
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