On the eigencharacteristics of an axially vibrating viscoelastic rod carrying a tip mass and its representation by a single degree-of-freedom system

The present note deals with the derivation of the characteristic equation of an axially vibrating viscoelastic rod (Kelvin–Voigt model), carrying a tip mass. Further, it is attempted to represent this continuous system by an “equivalent” spring-damper-mass system. Then, the “first” eigenvalues of these systems are calculated and tabulated for a wide range of the nondimensional mass parameter.