Identification of Cracking in Beam Structures Using Timoshenko and Euler Formulations

Timoshenko and Euler beam formulations, using energy approach, have been used to estimate the influence of crack size and location on the natural frequencies of cracked beams. Fracture mechanics approach has been used to consider the effect of cracking on the dynamic response of the beam. Galerkin's approach has been used to solve the problem numerically. It is shown that for slender beams the deep beam influence is felt only when the [(basicbendinglength)/h] ratio of the fundamental sinusoid of a beam becomes very small for higher modes. When the (l/h) ratio becomes small (10; but when l/h