Counter-propagation of harmonic waves in exponentially graded materials

Counter-propagation and interaction of two ultrasonic harmonic waves in strongly inhomogeneous exponentially graded material is studied. Deformations of a specimen with two parallel boundaries are described by the five-constant nonlinear theory of elasticity. One-dimensional problems are investigated in detail. The influence of material properties variation on the profile of boundary oscillations is clarified. The obtained results will be useful in ultrasonic nondestructive material characterization.