Determination of the Shape Function of a Multiple Cracked Beam Element and Its Application for the Free Vibration Analysis of a Multiple Cracked Frame Structure

Abstract

Assessment of the behavior of damaged structures as well as determination of the locations and the depths of cracks in multiple cracked structures are very important and attractive for many researchers. This article presents some results on the determination of the vibration shape function of a multiple cracked elastic beam element, which is modeled as an assembly of intact sub-segments connected by massless rotational springs. Algorithms and computer programs to analyse changes of natural mode shapes of multiple cracked beams have been determined. Numerical analysis of natural mode shapes of cracked simple support beams using the obtained expression shows a good agreement in comparison with the well-known analytical methods. The methodology approach and results presented in this article are new and the basis for building an efficient method to identify cracks in frame structures using wavelet analysis of mode shapes.