Counter-propagation of two longitudinal waves in a weakly inhomogeneous nonlinear elastic material is studied. An analytical description of the wave propagation, reflection and interaction process is derived. Oscillations on the parallel boundaries of the material are investigated in detail. The phenomenon of resonance of the boundary oscillation amplitude is observed. The resonance value is sensitivity to the wave excitation amplitude and frequency and to the material properties. The results of numerical simulations verify the idea to use the phenomenon of wave interaction resonance in the algorithm of the resonance method for nondestructive evaluation of the properties of weakly inhomogeneous nonlinear elastic material.
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