Tale of Two Approaches: The Response of a Beaded Spring

摘要

Two distinct approaches are employed to derive the coplanar response of a beadedstring. In the first approach the beads are modeled by the localized impedances that they present to the string. In the second approach the portion of the string between adjacent heads is assigned to be a one-dimensional dynamic system. Adjacent dynamic systems are coupled at the location of the bead they share. The two approaches derive expressions for the response that do not reconcile term by term. However, the expressions are shown to yield identical results by performing a number of challenging computer experiments using the two models and then comparing corresponding data.