Using vibration data to estimate buckling loads is proven effective for a wide range of structures, including rods, plates, and shells. The Arbelo formulation of the vibration correlation technique improves prediction reliability for cylindrical and spherical shells. In this study, we introduce a simplified variant of the Arbelo approach that provides higher prediction accuracy while requiring significantly lower pre-load levels. We define a new parameter, the Stiffness Decay Index (SDI), to characterize stiffness degradation by normalizing the loaded natural frequency with respect to the unloaded state. This metric enables accurate buckling prediction without causing structural damage or permanent deformation. We evaluate SDI numerically and experimentally for multiple isotropic geometries and demonstrate its advantages over the Arbelo method, particularly for ellipsoidal domes subjected to external pressure. We conduct experiments on rods, plates, oblate shells, and beverage cans to measure frequency shifts under pre-loading. The results show that when load data above 50% of the critical value is available, the SDI approach predicts the buckling load with accuracy exceeding 90%. These findings confirm that SDI, by directly correlating vibration response with stiffness loss, provides superior buckling-load prediction and serves as a reliable, non-destructive alternative to the Arbelo vibration-correlation method.