NATURAL FREQUENCIES AND MODES FOR THE FLEXURAL VIBRATION OF A CRACKED BEAM

The natural frequencies and models for the flexural vibration of a beam due to the presence of transverse cracks are determined using the Rayleigh-Ritz method. A beam with a single-sided crack or a pair of double-sided cracks is modeled as two separate beams divided by the crack. Two different sets of admissible functions which satisfy the respective geometric boundary conditions are then assumed for these two fictitious sub-beams. The rotational discontinuity at the crack is modeled by a torsional spring with an equivalent spring constant for the crack. The equality for the transverse deflection at the crack is enforced by a linear spring of very large stiffness. Numerical results are presented for beams with double-sided and single-sided cracks.