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

In this paper, a method of modelling for transverse vibrations of a geometrically segmented slender beam, with and without a crack normal to its axis, has been proposed using the Frobenius technique. There are two segments; one segment is uniform in depth and the other segment has a linearly variable depth. The thickness is uniform along the whole length. In the presence of 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 forward problem, the frequencies can be determined by giving the rotational spring sti€ness as an input. In the inverse problem, the method can be employed to detect the location and size of a crack by providing the natural frequencies as an input. A number of numerical examples are presented to demonstrate the accuracy of the method. Wherever possible, results have been compared with analytical solutions available in the literature. In the remaining cases, the results are found to be in very good agreement with ®nite element solutions. In the inverse problems, the error in prediction of crack location is less than 3% and that in size is around 25%.