Interesting effects of harmonically scattered waves from 1D functionally graded nonlinear inclusions

Abstract

The interaction of monochromatic elastic waves with nonlinear inclusions shows the presence of harmonically scattered waves. Challenges in obtaining theoretical solutions and limitations of conducting experiments to understand harmonic scattering of the nonlinear waves from functionally graded materials motivate us to conduct numerical experiments. Harmonic scattering of the elastic waves from highly local functionally graded nonlinear inclusions is exploited in this study to propose a novel building block of new nonlinear metamaterials that can effectively control harmonic responses. The simple, commonly observed, unique spatial distribution of the nonlinear parameters is proposed so that the area under the distribution remains the same for a constant-sized inclusion. Despite different spatial distributions, these functionally graded distributions show the same harmonic responses of both forward and backscattered waves during the interaction of monochromatic waves and one-way two-wave mixing. The amplitudes of all possible combinations of harmonics remain the same as long as the area under the spatially distributed nonlinear parameters curve, irrespective of the distribution curves. Reducing the area under the curve of the functionally graded nonlinear inclusion simply by reducing the maximum value of the functionally distributed nonlinear parameters, a decrease in the amplitudes of the harmonics is demonstrated.