Determination of Inhomogeneous Properties of Materials By Analysis of Ultrasonic Wave Motion

Longitudinal wave motion in weakly inhomogeneous nonlinear elastic materials is considered theoretically. The one-dimensional equation of motion which reflects the space-dependent properties of the material is solved by making use of the perturbation method. The solution describes the propagation and reflection of a harmonic burst that travels twice back and forth within the specimen thickness. The analysis of the analytical solution enables to pose and solve inverse problems of determining the functionally graded material properties.