Identifying Nodes and Anti-Nodes of a Longitudinally Vibrating Elastic Rod Carrying a Lumped Mass

Abstract

Following a recently developed methodology, the location of the nodes and anti-nodes of a complicated structure can be determined by attaching a virtual element (a lumped mass or grounded spring) to the system of interest and analysing the free vibration of this combined system as a function of the location of the virtual element. The system of an axially vibrating elastic rod carrying a mass in-span has been investigated as an example via the virtual mass approach. In the present study, the virtual spring approach is applied to the same system in order to verify the results of this method.