A study of vibration of geometrically segmented beams with and without crack

In this paper, a method of modelling for transverse vibrations of a geometr ically segmented slender beam, with and without a crack normal to its axis, has been proposed using the Frobenius technique. There are two segments; o ne segment is uniform in depth and the other segment has a linearly variabl e depth. The thickness is uniform along the whole length. In the presence o f a crack, the crack section is represented by a rotational spring. Thereby , it is possible to solve both the forward and inverse problems. In the for ward problem, the frequencies can be determined by giving the rotational sp ring stiffness as an input. In the inverse problem, the method can be emplo yed to detect the location and size of a crack by providing the natural fre quencies as an input. A number of numerical examples are presented to demon strate the accuracy of the method. Wherever possible, results have been com pared with analytical solutions available in the literature. In the remaini ng cases, the results are found to be in very good agreement with finite el ement solutions. In the inverse problems, the error in prediction of crack location is less than 3% and that in size is around 25%. (C) 1999 Elsevier Science Ltd. Air rights reserved.