Determination of mode shapes of a multiple cracked beam element and its application for free vibration analysis of a multi-span continuous beam

Abstract

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 analyze changes of natural mode shapes of multiple cracked beams have been carried out. 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 basis for building an efficient method to identify cracks in beam structures using wavelet analysis of mode shapes.