Lumped biodynamic models

Simple Lumped Models. At frequencies up to several hundred hertz, the biodynamic response of the human body can be represented theoretically by point masses, springs, and dampers, which constitute the elements of lumped biodynamic models. The simplest one-dimensional model consists of a mass supported by a spring and damper, as sketched in Fig. 10.6, where the system is excited at its base. The equation of motion of a mass m when a spring with stiffness k and damper with resistance proportional to velocity, c, are base driven with a displacement x it) is ... 

FIGURE 10.6 Smgle.degieeK>f-fi elumped-parameter biodynamic model. The mass m is supported by a spring with stiffness k and viscous damper with resistance c. The transmis-sibility of motion to the mass is shown as a function of die fiequency ratio r (=aj/oib) when the base is subjected to a displacement (After Griffin, 1990.)... 

FIGURE 10.7 CompaTison between predicted and observed apparent mass. The mean, nonnalized apparent masses of 60 subjects, 1 standard deviation, are shown by the continuous lines, and the prettictions of a sinj e-d iee-of-hreedom, lumped parameter biodynamic model by the dashed line. Fairley et at., 1989.)... 

FIGURE 10.8 Three-degree-of-fteedom, lumped-parameter biodynamic model of the seated human body for estimating mechanical impedance, apparent mass, and transmissibility, for vertical vil tion. The model is driven at the base (x ), and the transmissibility is calculated to the head, mass m2. (ISO 5982,2001.)... 

---