Low-frequency features of the ultrasound echo from an adhesively bonded layer-substrate structure

The low-frequency features of the ultrasound reflection spectra from the structure of a single layer on a substrate bonded by a thin adhesive layer are theoretically studied; the low-frequency here means the frequency of the interrogating ultrasonic wave is less than the quart-wavelength resonance frequency of the adhesive layer. The possibility of the inversion of the thickness and the evaluation of the cohesion strength of the adhesive layer from the resonance frequency shifts of the layered system is indicated. An analytic solution to the nonlinear equation satisfied by the resonance frequency is presented by Taylor expansion method showing satisfactory agreement with the numerical results by Newton iterative method. The results indicate larger range for application than the traditional spring model for the thin adhesive layer. In a much lower frequency range the thin adhesive layer may be regarded to be a spring.