Vibratory Characteristics of Euler-Bernoulli Beams with an Arbitrary Number of Cracks Subjected to Axial Load

A simple and efficient analytical approach for determining the vibrational frequencies and mode shape functions of beams with an arbitrary number of non-breathing cracks when subjected to axial loading is presented here. The local compliance induced by a crack is described using the rotational spring model. A set of boundary conditions are used as initial parameters to define the mode shape of the segment of the beam before the first crack. Using this, the remaining set of boundary conditions and the recurrence formula developed in the study, the mode shape function of vibration of a beam containing multiple cracks can be easily determined. Five different end conditions are considered: Pinned-pinned, clamped-pinned, clamped-free, clamped-clamped, and spring-spring (with concentrated masses). Three crack depths and seven axial force levels are used to represent service load conditions. A parametric study, to investigate the effects of crack and axial load on the vibrational properties of cracked beams, is carried out for each support condition case. The influence of cracks on the buckling load of a beam is also studied. Some of the results obtained are checked against published values, and a good agreement can be seen. The study concludes that the crack location, crack severity and axial force level all strongly affect the eigenfrequencies.