Vibration analysis of multiple-cracked non-uniform beams

This paper presents the energy-based method for the vibration identification of non-uniform Euler–Bernoulli beams having multiple open cracks. The method includes significant modifications for the energy-based method presented by Yang et al. [Crack identification in vibrating beams using the energy method, Journal of Sound and Vibration 244 (2) (2001) 339–357.] The distribution of the energy consumed is determined by taking into account not only the strain change at the cracked beam surface as in general but also the considerable effect of the stress field caused by the angular displacement of the beam due to bending. The Rayleigh–Ritz approximation method is used in the analysis. The method is adapted to the cases of multiple cracks with an approach based on the definition of strain disturbance variation along the beam. Examples are presented on cantilever beams having different truncation factors. When the results are compared with a commercial finite element program and with the results of Zheng and Fan [Natural frequencies of a non-uniform beam with multiple cracks via modified Fourier series, Journal of Sound and Vibration 242 (4) (2001) 701–717], good agreements are obtained. The effects of truncation factors and positions of cracks on the natural frequency ratios are presented in graphics.