Vibration based methods for Non-destructive prediction of Buckling loads

Using vibration data for prediction of buckling loads have been proven effective for various geometries including rods, plates and shells. The Arbelo approach of the vibration correlation method is derived to improve the reliability of the prediction for cylindrical and spherical shell structures. In this work, a more simplified form of the Arbelo approach is proposed which has higher prediction accuracies of the buckling with lesser pre-load levels. A parameter called Stiffness Decay Index (SDI) is introduced as a measure of the stiffness degradation by normalizing the loaded natural frequency with respect to the unloaded state, offering an effective means of buckling prediction with improved accuracy and without causing any damage or permanent deformation to the structure. Numerical and experimental evaluations of the Stiffness Decay Index are carried out for various geometries. The advantages of using SDI in place of the Arbelo approach of the vibration correlation technique are explored for ellipsoidal domes subjected to external pressure. Experiments are conducted to measure the natural frequencies of preloaded geometries including rod, plate, oblate shells and beverage cans. All the geometric materials considered in this work are isotropic in nature. The results demonstrate that, with a load dataset of more than 50%, the SDI approach can predict the critical buckling load with a promising accuracy of over 90%. These findings confirm that the SDI approach, by correlating vibration response with stiffness degradation, provides a better accurate prediction as compared to the Arbelo method of the vibration correlation technique.