Generalization of Colinear Collision Model Development Using the Admittance Analogy

Jai Singh

Abstract: Collisions that are inherently colinear in nature or that can be modeled as such represent a common configuration encountered in accident reconstruction practice. When mathematical models, based upon the relationship between the time parametric collision force and deflection response are utilized, they tend towards simplicity, based, in part, upon the typical scope and extent of evidence that is readily available following such collisions under field and subsequent conditions. Within the boundaries of these limitations, one may readily posit models of greater complexity, which in turn allow for the modeling of additional collision associated phenomenon. Presented in the subject work, predicated upon the admittance and force-current analogies, is a generalized solution for the determination of the Laplace domain transfer function, with simultaneous determination of the Laplace domain forcing functions secondary to initial conditions. Furthermore, the generalized solution is appropriate for both the closure and the separation phases of a collision. This generalized solution is appropriate for uniaxial collision modeling for a system consisting of two discrete masses connected in series at a massless interface by means of linear springs and linear dampers. The general solution is validated by comparing the results generated for four distinct cases against the results, for each case, based upon evaluation of the underlying differential equations of motion and force balance constraint equation.

Keywords: Accident reconstruction, colinear collision analysis, impedance modeling, Laplace domain