Analysis of the ultrasonic resonance test for a plate with a thin layer

The resonance frequencies of a plate with a thin layer are studied in the paper, their shift phenomenon due to the variations of the thickness or other acoustical properties of the thin layer is observed. In the range 0 ≤ ω<c₂/d₂ arctan(Z₁/Z₂), the half-wavelength resonance frequencies of the plate shift down due to the existence of the thin layer. Specially, the frequency-shift is linearly with the mass ratio of the thin layer to the plate in the first approximation. An ultrasonic technique is proposed for the measurement of the thin layer thickness based on the theory, and the thickness of the polymer layer (54-324 μm) beneath an aluminum substrate (6.24 mm thick) is measured by it, the measured relative errors of the thin layer thickness are less than 6%, which confirms the correctness of the theory, and furthermore, the validity of the technique based on it.