Inverse method for evaluation of elastic parameters in functionally graded materials using ultrasonic Love wave

The aim of this study was to evaluate the inverse procedure to determine profiles (as a function of depth) of the mechanical properties of inhomogeneous FGM resulting from the application of various technological processes of surface treatment. First, the Direct Sturm-Liouville Problem for Love waves propagating in elastic graded materials with various profiles of the shear stiffness as a function of the distance from the surface, has been solved using the Finite Difference Method and Transfer Matrix Method (Haskell-Thompson method). Love wave dispersion curves were evaluated in the frequency range from 4 to 23 MHz. The Inverse Problem was formulated as an Optimization Problem with appropriately constructed objective function that depended on the material properties of an elastic waveguide of the Love wave and the experimental data. To minimize the considered objective function, optimization procedures of the Nelder-Mead type from Scilab software package were employed.