On the eigencharacteristics of multi-step beams carrying a tip mass subjected to non-homogeneous external viscous damping

Two methods were employed for computing the eigencharacteristics of a continuous beam, carrying a tip mass, consisting of several parts having different physical parameters, and subjected to external viscous damping. Both methods used the separation of variables approach and differed in the solution of the corresponding ordinary differential equations. Due the presence of external viscous damping, it was found to be appropriate to work with complex variables. Comparison of the overdamped eigenvalues revealed that the attachment of the tip mass caused the eigenvalues to be greater in absolute values which increased the damping effect.