A CONTINUOUS CRACKED BEAM VIBRATION THEORY

A continuous cracked beam vibration theory is developed for the latera l vibration of cracked Euler-Bernoulli beams with single-edge or doubl e-edge open cracks. The Hu-Washizu-Barr variational formulation was us ed to develop the differential equation and the boundary conditions of the cracked beam as a one-dimensional continuum. The displacement fie ld about the crack was used to modify the stress and displacement fiel d throughout the bar. The crack was modelled as a continuous flexibili ty using the displacement field in the vicinity of the crack, found wi th fracture mechanics methods. The results of two independent evaluati ons of the lowest natural frequency of lateral vibrations for beams wi th a single-edge crack are presented: the continuous cracked beam vibr ation theory developed here, and a lumped cracked beam vibration analy sis. Experimental results from aluminum beams with fatigue cracks are very close to the values predicted. A steel beam with a double-edge cr ack was also investigated with the above mentioned methods, and result s compared well with existing experimental data. (C) 1998 Academic Pre ss.