Crack identification in beams

Crack in any structure changes the dynamic behaviour of the structure and by examining this change location and severity of the crack can be identified. Non-destructive testing (NDT) methods are used for detecting the location and severity i.e. crack size but these techniques are costly and time consuming. Modal parameters like natural frequency, mode shape can be used to detect the crack in beams. The present work is aimed for detection of open transverse crack in a Euler Bernoulli beam. The crack considered is an open crack and the analysis is made for linear behaviour of the beam. Finite element method is adopted for the dynamic analysis of the beam. Additional flexibility coefficients of the cracked beam element are computed using 6-point Gaussian quadrature and theories of fracture mechanics. The total flexibility matrix is obtained by adding the additional flexibility coefficients to the intact element flexibility matrix. Then from the total flexibility matrix, overall flexibility matrix is obtained. Stiffness matrix of the cracked element is derived from the overall flexibility matrix of the element for the analysis of an Euler Bernoulli beam. The first four natural frequencies and the corresponding mode shapes of vibration are obtained by dynamic analysis solving the Eigen value problem using a FORTRAN code. These natural frequencies are used for the crack detection. 3D graphs of normalized frequency (cracked beam frequency/intact beam frequency) in terms of crack depth and crack location are plotted. The intersection of these contours gives the crack depth and crack location.