Thickness determination of a multilayered system of different materials by natural frequencies

This paper is focusing on the relationship between the natural frequencies of a multilayered system of different isotropic elastic materials and the thickness of each layer. A relevant ultrasonic method for thickness determination of a multilayered system by natural frequencies has been developed. The natural frequencies are numerically calculated from the normally incident reflection coefficient of a "steel‐epoxy resin‐aluminum‐thin polymer" structured lamination. Some natural frequencies are sensitive to one layer thickness in certain range while the others are invariable. This phenomenon is explained by the defined strain energy ratio, and used for our thickness inversion. The measured natural frequencies of a specimen show good agreement with the theoretical ones. All the natural frequencies are taken into account, and the simulated annealing method is employed for the thickness inverse calculation of the multilayered structure. The average relative errors of calculated thickness of the each layer are...