Free Vibration Analysis of a Beam With an Attached In-Span Beam With Tip Mass

A double-beam system is used to model a single conductor transmission line with a stockbridge damper. The base beam represents the conductor and is subjected to an axial tensile load. The in-span beam with a tip mass at each end models the Stockbridge damper and it is arbitrarily attached to the base beam. Using Hamilton’s principle, the system equations of motion are derived and an expression is presented for the frequency equation. The formulation is validated with finite element results in the literature. Parametric studies are done to investigate the influence of the flexural rigidity and location of the in-span beam on the lowest five natural frequencies of the system. Investigation is also performed to examine the effect of the distance separating to two beams.