Free vibration analysis of axially moving beams using the transfer matrix method

Abstract

A tractable transfer matrix method based on the classical beam theory is developed and is subsequently used to investigate the effects of the axial tensile load and moving speed on the natural frequencies of axially moving beams under three different end conditions. The differential equation for the proposed method is solved in a closed analytical form. The transfer matrix method is derived from the relationship between displacements and forces specified at both ends of the axially moving beam. The accuracy of the method is validated through a comparison between the predicted results and those of previous studies. The critical speed for the fundamental frequency of an axially moving beam is analyzed by investigating the moving speed value in the vicinity of divergence instability. The numerical results for the end conditions considered provide useful information for capturing the divergence instability.