Vibration of rotating Timoshenko beams with centrifugal stiffening and specified torque or velocity profiles

摘要

A flexible beam with a tip mass and attached to a rotating base is modelled to include the tensile forces due to centripetal acceleration. The equations of motion are derived using the extended Hamilton's Principle and an approximate solution is approached via the Rayleigh-Ritz method. The system is simulated for both a prescribed torque profile and a prescribed velocity profile. The results indicate that the beam stiffens when these tensile forces are included. This is evidenced by an increased frequency and reduced amplitude of the flexural vibration of the beam.