Model for thickness measurements of steel plates using half-wave resonances

Previously reported measurement have shown how air-coupled ultrasound transmission measurements can be used to measure the thickness of steel plates, resolving thickness variations down to 0.2 mm. Simple plane wave theory predicts that at normal incidence, the steel plate is excited into compressional resonances when the plate thickness is an integer number of half-wavelengths. No shear waves are excited at normal incidence. The plate investigated previously had thickness 10.15 mm, with half-wave resonances expected at 288.18 kHz and 576.35 kHz. Transmission measurements on this plate showed resonance peaks at 267.33 kHz, 464.63 kHz and 571.98 kHz. The former and latter values deviate by 7% and 0.7%, respectively, from the values predicted by the plane wave model. The peak at 464.6 kHz was assumed to be due to the third harmonic resonance of the shear wave, but this was not confirmed.