Free Vibration of Stepped Beam with Multiple Transverse Cracks

Abstract

The present study outlines free vibration analysis of uniform and stepped beam subjected with single to multiple cracks using Finite Element Method (FEM) in MATLAB environment. The crack considered is transverse crack which open in nature. Due to the presence of crack, the total flexibility matrix is established by adding local additional flexibility matrix to the flexibility matrix of the corresponding intact beam element .The local additional flexibility matrix is obtained from Linear Elastic Fracture Mechanics theory. An experimental study is carried out to check the accuracy of the numerical results. Mild steel specimens of square area of cross section are considered for the experiment and the experimental results are compared with numerical analysis using Finite Element Method (FEM) in MATLAB environment. The results obtained from experimental are checked for accuracy with the present analysis by plotting non-dimensional frequencies for first three modes as function of crack depth ratios for different locations of cracks.