On the consideration of the masses of helical springs in damped combined systems consisting of two continua

This study is concerned with the establishment of the characteristic equation of a combined system consisting of a cantilever beam with a tip mass and an in-span visco-elastic helical spring-mass,<br />considering the mass of the helical spring. After obtaining the ?exact? characteristic equation of the combined system, by making use of a boundary value problem formulation, the characteristic equation is established via a transfer matrix method, as well. Further, the characteristic equation of a reduced system is obtained as a special case. Then, the characteristic equations are numerically solved for various combinations of the physical parameters. Further, comparison of the results with the massless spring case and the case in which the spring mass is partially considered, reveals the fact that neglecting or considering the mass of the spring partially can cause considerable errors for some combinations of the physical parameters of the system.