Calculating the Time-Histories of Impacting Systems Described by Their Receptances

The behavior of impacting systems is highly nonlinear and generally numerical analysis must be resorted to if a quantitative description of the behavior of such systems is required. However, the behaviour of the individual subsystems is often reasonably linear and this along with the fact that the subsystems come into contact when the relative displacements between contact points is zero make it convenient to base the analysis on the receptances, that is, the displacement-force frequency response functions, at the contact points. The procedure for doing this is described with reference to a lumped parameter model. Simple formulae are developed to aid the numerical analysis. The extension of the method to consider continuous systems and those defined by measured receptances is described and examples based on numerically derived and experimentally derived receptances are given.