Sound Scattering by a Thermoelastic Ball with a Continuously Inhomogeneous Coating in a Heat-Conducting Fluid

Abstract

Direct and inverse problems on the diffraction of a plane harmonic sound wave on a thermoelastic ball with a coating in the form of a radially inhomogeneous thermoelastic spherical layer bounded by inviscid heat-conducting fluid are solved. Oscillations of the coated ball are considered in terms of a linear model of coupled thermoelasticity. The wave fields are determined in the spherical body and outside it. The calculation results are presented for the frequency and angular dependences of the amplitude of a scattered acoustic field in the far zone. The significant difference between the sound scattering characteristics for thermoelastic and elastic bodies is shown. The coating is simulated to provide the least sound scattering in the given frequency range and angular observation sector. Functionals expressing the intensity of the sound reflection are constructed and an algorithm for their minimization based on a combination of random search and coordinate descent methods is presented. The heterogeneity patterns of a thermoelastic coating with the optimal sound reflecting properties are found.