Contour Line Method of Crack Identification for a Circular Cross Section Beam Based on Modal Shape

Under the action of external loads, crack initiation and propagation are easy to occur in a beam component. The purpose of this article is to study a contour line method of crack identification for a circular cross section beam by the modal shape. Firstly, the stiffness matrix of uncracked element and cracked element is derived. Then, the vibration differential equation of a cracked circular cross section beam is solved. It is found that the crack condition plays a certain role on the modal shape. Thereafter, the first three modal shape mutation response surfaces with different crack position ratios and different crack depth ratios are studied. Subsequently, the contour line method of crack identification based on modal shape is proposed. Results indicate that the prediction error of crack depth and crack position is zero for the crack identification of single cracked circular cross section beam. But the error of crack depth prediction is less than 2%, and the maximum error of crack position prediction is less than 2% for the crack identification of double cracked circular cross section beam.