Numerical study on complex shaped cracks in cantilever beams concerning frequency and stiffness changes

Abstract

The paper presents a mathematical relation to express the effects of a T-shaped crack on beam-like structures. The study is performed by using the finite element method (FEM) and contrived analytical formulas for proving the existing correlation between deflection, strain energy, and natural frequency changes. The damaged beam static and dynamic behaviors are analyzed by means of the FEM. The frequency shift for the first mode of vibration derived directly was compared with the frequency alteration calculated involving the change in the beam deflection for several scenarios of the T-shaped crack. The frequency shift is derived using the relations between deflection and natural frequency. As the final step in the research, we compared the outcomes for the same crack with the results achieved from a beam suffering a loss of stiffness.

Evaluating the severity of transverse cracks in beam-like structures by using an energy loss method

“…The method for determining the modal curvature and natural frequency caused by a crack, with a known position x, is given in papers [12,13,14,15]. In the current paper, the analysis was performed for damages reducing the rigidity of a cantilever beam subjected to the highest bending moment.…”

Sensitivity analysis for frequency-based prediction of cracks in open cross-section beams

“…Although open cross-section beams are often used in engineering structures, there are few studies that address the detection of cracks by vibration analysis for these types of structural elements, see for instance [15]. The intention of the authors is to investigate the behavior of I-beams with longitudinal cracks by involving numerical methods since these have been proved as reliable and versatile [16]. In addition, these methods can highlight the small frequency changes that are expected, and which are difficult to be observed in the initial stage of research by experiments.…”