Wave interaction resonance in weakly inhomogeneous nonlinear elastic material

Simultaneous propagation and interaction of two longitudinal waves with smooth arbitrary initial profiles in a weakly inhomogeneous physically nonlinear elastic material is studied theoretically. A perturbation solution to the problem is derived. Interaction of harmonic waves in the material with polynomial inhomogeneity in density, in linear and nonlinear elastic properties is investigated in detail. The frequency scan detects the resonances (extremal values) of the amplitudes of oscillations on the parallel boundaries of the material. These resonances are sensitive to the wave excitation amplitude and material properties. This phenomenon is illustrated numerically. The wave interaction resonances may be used for nondestructive evaluation of the inhomogeneous properties of the nonlinear elastic material.