In-plane vibrations of cracked slightly curved beams

In-plane vibrations of slightly curved beams having cracks are investigated numerically and experimentally. The curvature of the beam is circular and stays in the plane of vibration. Specimens made of steel with different lengths but with the same radius of curvature are used in the experiments. Cracks are opened using a hand saw having 0.4 mm thickness. Natural frequencies depending on location and depth of the cracks are determined using a Bruel & Kjaer 4366 type accelerometer. Then the beam is assumed as a Rayleigh type slightly curved beam in finite element method (FEM) including bending, extension and rotary inertia. A flexural rigidity equation given in literature for straight beams having a crack is used in the analysis. Frequencies are obtained numerically for different crack locations and depths. Experimental results are presented and compared with the numerical solutions. The natural frequencies are affected too much due to larger moments when the crack is around nodes. The effect can be neglected when it is at the location of maximum displacements. When the crack is close to the clamped end, the decrease in the frequencies in all modes is very high. The consistency of the results and validity of the equations are discussed.