Study on Modal Shape of the Vibration of an Axially Moving Cantilever Beam with Tip Mass

Abstract

The transverse vibration equation of an axially moving cantilever beam with tip mass is given. The instant linearized equations are set up based on Galerkin’s method. The tip mass influences to the first three order modes of the beam are computed. The calculated responses using the modes with tip mass are compared with the results using the modes without tip mass. Modes without tip mass can replace the modes with tip mass while the tip mass is small. The heavier the tip mass is, the bigger the difference of using the replacement is. It is found that the experimental result is fit well with the theoretical result using the modes with tip mass.