Dynamic characteristics of an axially moving Timoshenko beam under axial loads

The effects of axial load on vibration characteristics of an axially moving Timoshenko beam were investigated. The governing differential equation for transverse vibration of the axially moving beam under axial load was established based on Timoshenko beam theory and Hamilton's principle. The dynamic characteristics of the beam under axial load and pinned-pinned boundary conditions were investigated. The dimensionless frequencies of the beam versus axial load were calculated numerically using the differential quadrature method (DQM), and they were compared with the analytical solutions for verification. The results showed that under the condition of no load, the larger the slendness ratio of the beam, the easier the beam reaches unstable state; the beam reaches unstable state easier under compressive load than it does under tensile load; the critical speed of the beam decreases with increase in the absolute value of axial load. Through studying the influence factors and the relationship between the critical speed and the critical load of the beam, the results provided a guid for the design of axially moving systems under axial load. © 2016, Editorial Office of Journal of Vibration and Shock. All right reserved.