Torsional vibration of cracked beams of non-circular cross-section

The equation of motion and associated boundary conditions are derived for a uniform beam of non-circular cross-section which is subjected to torsional vibration and which contains one or more pairs of symmetric cracks. The procedure is to use the Hu-Washizu variational principle which requires plausible assumptions about the displacement, momentum, strain and stress fields to be chosen. The perturbation in the stress and strain distributions of the beam due to the presence of the cracks is incorporated through local functions which have their maximum value at the cracked section and which decay exponentially from the crack location. The rate of exponential decay can be evaluated from experimental tests. The fundamental torsional frequency of the beam is computed for various depths of crack using the theoretical model. These predictions are then compared with results obtained from experiments on beams which contain cuts to simulate the cracks. It is found that the theoretical predictions closely match the experimental results.