Approximate calculation of the fundamental frequency for bending vibrations of cracked beams

A simplified method of evaluating the fundamental frequency for the bending vibrations of cracked Euler-Bernouilli beams is presented. The method is b ased on the well-known approach of representing the crack in a beam through a hinge and an elastic spring, but here the transverse deflection of the c racked beam is constructed by adding polynomial functions to that of the un cracked beam. With this new admissible function, which satisfies the bounda ry and the kinematic conditions, and by using the Rayleigh method, the fund amental frequency is obtained. This approach is applied to simply supported beams with a cracked section in any location of the span. For this case, t he method provides closed-form expressions for the fundamental frequency. I ts validity is confirmed by comparison with numerical simulation results. ( C) 1999 Academic Press.