Multi-order spectral features of longitudinal-wave EMAT resonance for defect detection in ferromagnetic materials

Longitudinal-wave electromagnetic acoustic transducer (EMAT) resonance provides spectral responses across multiple resonant orders for defect characterisation in ferromagnetic materials, but defect-induced frequency shifts and energy redistribution can limit the reliability of single-peak indicators. This study develops a cross-order, multi-feature framework to examine how defect geometry influences these responses. A two-dimensional finite-element model of longitudinal-wave EMAT resonance, combined with Sobol low-discrepancy sampling, is used to generate cases involving different defects. Spectral features are extracted from the first eight resonant orders. The results reveal complementary, order-dependent signatures of frequency migration, energy redistribution, and spectral broadening. The fifth-order band provides a practical compromise among defect sensitivity, feature stability, and experimental measurability. Experimental measurements on defect-free and surface-thinning Q235 steel specimens show that these features can be extracted and exhibit defect-related changes. For the defect-free reference, centroid-frequency coefficients of variation remain below 5%. The thickness estimated from the spacing between adjacent resonant orders differs from the measured thickness by approximately 0.06%, providing a consistency check of the thickness-resonance mechanism rather than a measure of thickness-estimation accuracy. The proposed framework therefore provides complementary descriptors of defect-induced resonant responses, while further calibration and broader experimental validation are needed for quantitative assessment.