On prediction of crack in different orientations in pipe using frequency based approach

A technique based on measurement of change in natural frequencies and modeling of crack by rotational spring is employed to detect a crack with straight front in different orientations in a section of straight horizontal steel hollow pipe (outer diameter 0.0378 m and inner diameter 0.0278 m). Crack orientations in the range 0–60° with the vertical have been examined and sizes/depths in the range 1–4 mm through the wall of thickness 5 mm have been studied. Variation of rotational spring stiffness with crack size and orientation has been obtained experimentally by deflection and vibration methods. The spring stiffness reduces as expected, with an increase in crack size; it increases with an increase in the crack orientation angle. The crack location has been predicted with a maximum error of 7.29%. The sensitivity of the method for prediction of crack location on variations in experimental data has been examined by changing the difference between the frequencies of pipes with and without crack by ±10%. The method is found to be very robust; the maximum variation in location is 2.68%, which is much less than the change in frequency difference introduced.