Mathematical modelling for dynamic analysis of cracked L-shape beam

Abstract

In this paper, a finite element mathematical model to evaluate natural frequencies and Frequency Response Functions (FRFs) of an L-shaped cracked beam structure is established. Dynamics of L-shaped beam structure is a very challenging subject and very little information is reported in literature. L-shaped beam structure is assumed to be fixed at end of the vertical column and free at the other end of the horizontal column. Natural frequencies are evaluated using finite element method in MatLab and simulations using Ansys (Version 18.2) is carried out to validate the mathematical model. Totally 18 cases with different crack positions and three different crack depths are considered for the analysis. Results obtained by both methods are tabulated and find a very good agreement in the results. Reported results can be used as a benchmark for further study of crack propagation and fatigue failure analysis in built-up structures.