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

摘要

A simplified method of evaluating the fundamental frequency for the bending vibrations of cracked Euler-Bernouilli beams is presented. The method is based 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 cracked beam is constructed by adding polynomial functions to that of the uncracked beam. With this new admissible function, which satisfies the boundary and the kinematic conditions, and by using the Rayleigh method, the fundamental frequency is obtained. This approach is applied to simply supported beams with a cracked section in any location of the span. For this case, method provides closed-form expressions for the fundamental frequency. Its validity is confirmed by comparison with numerical simulation results.