Parametric Vibrations of Axially Moving Beams with Multiple Edge Cracks

Abstract

Nonlinear transverse vibrations of axially moving beams with multiple cracks is handled studied. Assuming that the beam moves with mean velocity having harmonically variation, influence of the edge crack on the moving continua are investigated in this study. Due to existence of the crack in the transverse direction, the healthily beam is divided into parts. The translational and rotational springs are replaced between these parts so that high stressed regions around the crack tips are redefined with the springs' energies. Thus, the problem is converted to an axially moving spring-beam system. The equations of motion and its corresponding conditions are obtained by means of the Hamilton Principle. In numerical analysis, the natural frequencies and responses of the spring-beam system are investigated for principal parametric resonance in detail. Some important results are obtained; the natural frequencies decreases with increasing crack depth. In case of the beam travelling with high velocities, the effects of crack's depth on natural frequencies seems to be vanished.

Transverse Vibration of Cracked Graded Rayleigh Beam with Axial Motion

“…By looking at the previous research that dealt with the moving beam issue, we did not find a researcher who has dealt with the subject of cracked moving beam except M. Sarigül [33] established the vibration equation of the axially moving beam that was exposed to multi crack by the Euler model. It evident from the results that the crack depth adversely affects the natural frequencies (meaning that the frequencies decrease when the cracking depth increases and vice versa), but when the axial velocity is too high, the crack depth influences will diminish.…”