Predicting the Impact Response of a Nonlinear Single-Degree-of-Freedom Shock-Absorbing System From the Measured Step Response

Abstract

We measured the step response of a surrogate human pelvis/impact pendulum system at force levels between 50 and 350 N. We then fit measured response curves with four different single-degree-of-freedom models, each possessing a single mass, and supports of the following types: standard linear solid, Voigt, Maxwell, and spring. We then compared model predictions of impact force during high-energy collisions (pendulum impact velocity ranging from 1.16 to 2.58 m/s) to force traces from actual impacts to the surrogate pelvis. We found that measured peak impact forces, which ranged from 1700 to 5600 N, were best predicted by the mass-spring, Maxwell, and standard linear solid models, each of which had average errors less than 3 percent. Reduced accuracy was observed for the commonly used Voigt model, which exhibited an average error of 10 percent. Considering that the surrogate pelvis system used in this study exhibited nonlinear stiffness and damping similar to that observed in simulated fall impact experiments with human volunteers, our results suggest that these simple models allow impact forces in potentially traumatic falls to be predicted to within reasonable accuracy from the measured response of the body in safe, simulated collisions.