Abstract
The nonlinear longitudinal wave propagation in weakly inhomogeneous elastic material with nonlinear physical properties is investigated theoretically. The analytical solution to the one-dimensional problem of nonlinear propagation of the wave with an arbitrary smooth initial profile is derived. The solution establishes the relations between the variable physical properties of the material and the wave characteristics. The possibility to utilize this solution in inhomogeneous elastic material characterization is considered on the basis of the model problem of sine-wave propagation. The material properties are described by polynomials with respect to the spatial coordinate. The dependencies of the sine-wave characteristics on the variable physical properties of the material are illustrated in numerous plots. The algorithm to nondestructive evaluation of the linearly variable properties of the elastic material is proposed.
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