VIBRATION OF CRACKED CIRCULAR PLATES AT RESONANCE FREQUENCIES

It is well known that the presence of cracks will affect the dynamic characteristics of the vibrating plate. Such a problem is complicated because it combines the field of vibration analysis and fracture mechanics. In this study, an optical system called the AF-ESPI method with the out-of-plane displacement measurement is employed to investigate the vibration characteristics of a free circular plate with a radial crack emanating from the edge. The boundary conditions along the circular edge are free. As compared with the film recording and optical reconstruction procedures used for holographic interferometry, the interferometric fringes of AF-ESPI are produced instantly by a video recording system. Based on the fact that clear fringe patterns will appear only at resonant frequencies, both resonant frequencies and corresponding mode shapes can be obtained experimentally at the same time by the proposed AF-ESPI method. Numerical finite element calculations are also performed and the results are compared with the experimental measurements. Good agreements are obtained for both results. The vibrating mode shapes obtained in this study can be classified into two types, symmetric and antisymmetric modes with respect to the crack line. The influence of crack length on resonant frequencies is also investigated in terms of the dimensionless frequency parameter (λ2) versus crack length ratio (a/D). We find that if the crack face displacement is out of phase, i.e., the antisymmetric type, a large value of stress intensity factor may be induced and the cracked circular plate will be dangerous, from the fracture mechanics point of view. However, there are some resonant frequencies for which the crack face displacements are completely in phase, i.e., the symmetric type, which yields a zero stress intensity factor and the cracked plate will be safe.