Damage modeling and simulation of vibrating pipe with part-through circumferential crack

A new finite element model is developed to perform vibration analysis of a cracked pipe. To formulate the method, the local flexibility coefficients of a part-through circumferential crack in a pipe that is subjected to axial force, shear force and bending moment are analytically derived using linear fracture mechanics. In particular, an adaptive Simpson method is utilized to carry out the numerical integration for calculating the flexibility coefficients. With the flexibility coefficients, a finite element model is established to study the vibration characteristics of the cracked pipe, with particular emphasis on the crack effect represented by change in natural frequency. As an illustrative application, the finite element model is utilized to identify a crack in a pipe by contour plots of frequency ratio as function of crack location and crack depth, with the crack location and depth identified accurately. The proposed method is effective in characterizing the vibration behavior of a pipe with a crack.