Experimental verification of a method of detection of multiple cracks in beams based on frequency measurements

Abstract

A method for prediction of location and size of multiple cracks based on measurement of natural frequencies has been verified experimentally for slender cantilever beams with two and three normal edge cracks. The analysis is based on energy method and representation of a crack by a rotational spring. For theoretical prediction the beam is divided into a number of segments and each segment is considered to be associated with a damage index. The damage index is an indicator of the extent of strain energy stored in the rotational spring. The crack size is computed using a standard relation between stiffness and crack size. Number of measured frequencies equal to twice the number of cracks is adequate for the prediction of location and size of all the cracks. The accuracy of prediction of crack details is encouraging. The maximum error in predicting location of cracks decreases with an increase in the number of cracks. It is less than 10% and 20% for two and three cracks respectively. The maximum error in predicting the crack size is less than 12% and 30% respectively for the two cases. A strategy to overcome failure in the prediction for cases with one of the cracks located near an anti-node has been suggested.