The structure and morphology of the reinforcing material play an important role in the vibration damping characteristics of polymer composites. In this work, multiwalled carbon nanotubes (MWCNTs) with different structures and morphologies are incorporated into a polymer matrix. The vibration damping characteristics of the nanocomposites, in Oberst beam configuration, are studied using a free vibration test in cantilever mode. Inner tube oscillation is established as the vibration damping mechanism by correlating the extent of the loss factor obtained from the two nanocomposites with the dissimilarities in the structure and morphology of the two varieties of MWCNTs. Inner tube oscillation is simulated using molecular dynamics (MD). Since the open-ended double walled CNT (DWCNT) models used in earlier studies over predict the damping, we propose a capped DWCNT model. This can simulate the atomic interactions at the end caps of the tube. This study indicates that the contributions to the observed damping have their origins in the interaction between atoms that constitute the inner and outer tubes rather than the inter-tube frictional energy loss. This journal is © The Royal Society of Chemistry.