On determination of the natural frequency of transverse and longitudinal vibrations of a cracked beam. Part 1. Analytical approach

摘要

We consider a perfectly elastic cantilever bean with a crack. The influence of the crack depth and location on the vibration mode of the beam is simulated by a local change in the cross section. This problem is solved by the Rayleigh method. Fairly simple formulas for the determination of the natural frequency of the first mode of bending and longitudinal vibrations of a cantilever beam with an open and closing crack are derived.