Vibration analysis of non-uniform beams having multiple edge cracks along the beamʹs height

Bending vibration of non-uniform rectangular beams with multiple edge cracks along the beamʹs height is investigated. These cracks are called height-edge cracks in this paper. The energy based method is used for defining the vibration of height-edge cracked beams. The opening form of the height-edge crack is determined when the external moment is assumed to be applied for stretching the beamʹs width. Strain energy increase is obtained by calculating the strain change at the stretched surface by taking into account the effect of angular displacement of the beam due to the bending. The Rayleigh–Ritz approximation method is used in the analysis. The cases of multiple cracks are analysed in the method by using the approach based on the definition of strain disturbance variation along the beam. Examples are presented on a fixed–fixed beam and several cantilever beams having different taper factors. When the results are compared with the results of a commercial finite element program, good agreement is obtained. The effects of taper factors, boundaries and positions of cracks on the natural frequency ratios are presented in graphics.