Modeling an Inhomogeneous Coating of an Elastic Sphere with the Required Sound Reflecting Properties

We consider the inverse problem of determining the covering inhomogeneity of an elastic sphere characterized by the minimal reflection of a plane sound wave in a preset angular sector and frequency range. Based on an analytic solution to the direct problem, a functional expressing the reflection’s intensity is constructed and an algorithm for its minimization is proposed. The analytic expressions describing the mechanical parameters of an inhomogeneous coating are obtained.