Prediction of impact forces using Hertzian contact theory and measured modal structural data

Abstract

A method is presented for predicting the impact force between a mass of known velocity and a structure using measured frequency response functions to characterise the dynamics of the underlying structure and a Hertzian model of the local contact stiffness at the point of impact. The method is applied by obtaining Laplace domain parameters determined by curvefitting the measured frequency response functions and writing linear state equations to characterise the structure. The non-linear contact stiffness is represented by a two parameter Hertzian model, identified by matching a predicted force pulse with a measured force pulse. It is shown that the non-linear dynamic characteristics of an elastomeric pad at the point of contact are modeled very satisfactorily by static Hertz theory during the deformation period and reasonably well during the restitution period of impact.