Crack modelling and detection in Timoshenko FGM beam under transverse vibration using frequency contour and response surface model with GA

In the present work, dynamic response of cracked Timoshenko beam with functionally graded material properties are obtained by a numerical technique using Ritz approximation. In order to verify the applicability and performance of the formulation, comparisons of the present numerical method with three-dimensional FEM models are made. Crack is assumed to be transverse and open throughout the vibration cycle. Two different crack detection techniques have been proposed. Results obtained by the numerical technique are used in both of the crack detection techniques. In the first technique, the frequency contours with respect to crack location and size are plotted and the intersection of contours of different modes helps in the prediction of crack location and size. In the second technique, crack is modelled using response surface methodology (RSM). The sum of the squared errors between the numerical and RSM regression model natural frequencies is used as the objective function. This objective function is minimised using genetic algorithm optimisation technique. Both the crack detection techniques and the numerical analysis have shown good agreement with each other.