Free vibration analysis of beams and frames with multiple cracks for damage detection

Abstract

The problem of calculating the natural frequencies of beams with multiple cracks and frames with cracked beams is studied. The natural frequencies are obtained using a new method in which a rotational spring model is used to represent the cracks. For beams, dynamic stiffness matrices of order 4 are obtained in a recursive manner, according to the number of cracks, by applying partial Gaussian elimination. The Wittrick–Williams algorithm is used to compute the natural frequencies in the resulting transcendental eigenvalue problem. Published numerical examples for cracked beams are used for validation. The global dynamic stiffness matrix of a frame with multiply cracked members is then assembled. A published two bay frame example is used to evaluate the new method. The effect of changing the location of a crack in a two bay two storey frame is studied numerically, giving insight into the inverse problem of damage detection.