Transverse impact of a linear three-element spring and dashpot model filament: theory

Abstract

The mathe matics of wave propagation in a viscoelastic filament subjec ted to cons tant veloc ity trans verse impact is di scussed. The equations gove rning the s tress·strain·time be hav io r a re as· s umed to be those for a linear model cons is ting of a spring coupled in parallel with a sp ring a nd dash· pot in ser ies . The nature of the solution is di scussed, and a method is desc ribed for calculating the configuration , and the s tress, s train, a nd particle ve locity di s tribut.ions along the impacted fil ament. The me thod used consists of a n integration along the cha racteri s tics of the s ys tem of differe nti al equations describing th e probl em.