Free vibration analysis of a cracked elastically supported beam

In this paper, closed-form expressions based on the Rayleigh's method is studied theoretically to evaluate the first two mode shapes and fundamental frequencies of a cracked elastically supported beam. Such a problem has not been very well investigated in the literature. The Euler-Bernoulli beam theory is employed to model the cracked beam and the crack is represented as a rotational spring. Some numerical examples are given to illustrate the proposed method and to present the effect of cracks on the natural frequencies and mode shapes of this cracked system. The results are compared with analytical, numerical and previous experimental studies. It is found that the present method is simpler in application, decreases the time and cost of computations, and shows a good promise for further development as a practical method to minimise the difference between measured and calculated results; also it can be an alternative solution in the case of crack identification for elastically supported beams.