An analytical two-step method for precise evaluation of local resonance frequencies for internal planar defects

Despite the effectiveness of methods based on local defect resonance (LDR) for the nondestructive evaluation of planar defects, the physical mechanism underlying the generation of LDR remains an ongoing topic of research interest. Existing methods for interpreting the generation of LDR are based on the vibration theory and simplified boundary conditions, but they demonstrate effectiveness for LDR frequency prediction only in defects within specific parameter ranges and lack universal applicability for both near surface and internal defects. A two-step approach is proposed in this investigation to understand the generation of LDR from the perspective of wave reflection and standing wave formation. In this approach, the interaction of guided waves with defect boundaries are analyzed using the normal mode expansion method, and thereby the phase shift of reflected wave modes is obtained. On this basis, the formation of standing waves is analyzed, and a quantitative relation between the defect parameters and LDR frequency can be obtained explicitly. The shape effect on the LDR frequency is then investigated via a Rayleigh method. The proposed approach provides an insight into the generation of LDR for both near surface and internal defects, and enables the quantitative evaluation of defects with circular and elliptical shapes using the LDR frequencies.