Modal and Buckling Analysis of a Cracked Cantilever Beam with Circular Cross Section

Abstract

Engineering structures have structural defects such as cracks due to long term services, vibrations and material non-uniformity. Cracks in structural members lead to local changes in their stiffness and consequently their static and dynamic behavior is altered. Cracked beam problem has grabbed the attention of many researchers in recent years. Analytical, numerical and semi-numerical methods have been developed during the years. The influence of cracks on free vibration and buckling load of the beam with a single transverse thorough surface crack using finite element method (FEM) is investigated in present work. In this study modal analysis of a cracked cantilever beam with circular cross section is analyzed for different crack positions and different crack depths using Ansys, Matlab and FFT Analyzer. Buckling analysis of the beam is also carried out using finite element method (FEM). Beam element of two degrees of freedom (transverse displacement and rotation) is taken for analysis. Stiffness matrix of intact beam element as well as the cracked beam element is computed from total flexibility matrix. Modal frequencies are verified using analytical and experimental procedures for different crack locations and different crack depths. Buckling load of the column is computed from the modal analysis.