The propagation and reflection of the ultrasonic tone burst in the strongly inhomogeneous exponentially graded material are studied. Deformations of a specimen with two parallel boundaries are described by the five constant nonlinear theory of elasticity. The one-dimensional problem is considered. The influence of the variation in material properties on the profile of boundary oscillations is clarified by parametric plots. The obtained results may be useful in the ultrasonic non\-destructive material characterization.
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