Determination of the behaviour of transverse vibration of a Timoshenko beam with an open crack of uniform depth

Abstract

Beams are widely used as structural elements and machine elements in civil, mechanical, naval and aeronautical engineering with quite complex design features. These structural and machine elements are designed for different load conditions, with good range of safety factors, and are inspected regularly. Still, unexpected and sudden failures occur due to the presence of flaws or cracks. This paper discusses the behaviour of a cracked Timoshenko beam under vibration. Particularly, the effect of crack depth and location along the beam length is treated and results obtained by the finite element method are presented. The effect of crack is introduced in the system by considering stress intensity factors at the crack tip for different crack modes which give the energy release rate due to the crack. The energy release rate is then used to determine the compliance of the cracked element from which the stiffness of the beam element can be determined.