Vibrations of L-Shaped Beam Structures With a Crack: Analytical Approach and Experimental Validation

Abstract

A crack on a structural member introduces a local flexibility which is function of the crack depth. This new flexibility condition changes the dynamic behavior of the structure. The knowledge of the influence of the crack on the characteristic dynamic parameters makes it possible to determine both the crack position and its magnitude. A large number of research papers have been written on the subject, most of them on straight beams of a single segment. However, despite the importance of L-shaped beams in a variety of technological applications, very limited information is available for the case of such structures. In this article, a cracked L-beam structure is studied by an analytical approach which is validated by experimental measurements. The Euler–Bernoulli beam theory is assumed to describe the transversal displacements and the crack is modeled by means of an elastically restrained hinge. A special device was designed to measure experimentally the natural frequencies of steel L-beams structures. The natural frequencies of in plane vibrations of L-beam structures are obtained considering a crack at different positions as well as of different depths. Values obtained with the analytical solution are satisfactorily compared with experimentally measured frequencies and the values reported in previous studies on the subject published by other authors.