On the eigencharacteristics of a cantilevered visco-elastic beam carrying a tip mass and its representation by a spring-damper-mass system

The present note is concerned with the derivation of the characteristic equation of a cantilevered, visco-elastic bending beam (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 non-dimensional mass parameter.