Abstract
This paper presents an estimation of natural frequencies for free vibration of a cantilever beam in the presence of an inclined edge crack using linear elastic fracture mechanics. The Strain Energy Release Rate (SERR) approach is employed to compute the compliance coefficients for the edge crack inclined to the longitudinal axis at an arbitrary angle. A full compliance matrix under the general loading is presented and corresponding definitions of the compliance coefficients are given. Calculations of natural frequencies are carried out for both Timoshenko and Euler-Bernoulli beams under the influence of load P1, P3, and P5. Contribution to strain energy coming from various modes of fracture is accounted for by using stress intensity factors obtained numerically using ABAQUS 6.14 software. The effect of the crack on transverse and longitudinal natural frequencies is studied for different crack locations, depths, and inclination angles. Experiments are performed on short and long beams for a set of parameters for comparison purposes. It is found that the natural frequencies estimated by the proposed method compare well with the frequencies obtained experimentally for both beams.
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