Força de radiação em uma esfera embutida em um sólido elástico

Abstract

The study related to the phenomenon of scattering of acoustic waves in solids has attracted the interest of the scientific community due to the numerous applications in the most diverse areas of science. To obtain the mechanical properties of the materials, various types of techniques can be used. For example, methods based on non-destructive tests. In particular, tests using ultrasound are based on the scattering of acoustic waves. The studies concerning the scattering of waves can be useful in the characterization of particulate composites and the development of implanted devices activated by the radiation force. For this reason, a theoretical study was carried out on the radiation force due to the spreading of an incident longitudinal plane wave in a homogeneous spherical inclusion embedded in a solid elastic matrix. In this study, we used the approximation at the Rayleigh limit, where the inclusion ray is considered to be much smaller than incident wavelength. The work was developed based on the general Hooke law, assuming that the components of stress are linearly related to those of deformation. We also used the method of partial wave expansion in spherical coordinates, concerning the incident and scattered waves. The solution of the equations is given in terms of vector spherical harmonics. The expressions for the displacement field are given regarding the scattering coefficients for monopole, dipole and quadrupole approximation, which will be used in the formulas of the acoustic radiation force. The analytical equation for the acoustic radiation force was calculated using the principle of the conservation of the linear momentum and then the efficiencies of absorption, scattering and radiation were also calculated. The efficiencies are dimensionless quantities that represent the absorbed, scattered and elastic radiation powers in the particle. In quadrupolar approximation, they are expressed in terms of contrast functions. These expressions were used to obtain the results from a numerical simulation, where two configurations were studied: high-density polyethylene (HDPE) particle, embedded in a solid matrix (border: solid-polymer); and an iron particle, embedded in a solid matrix (boundary: solid-solid) respectively. For each configuration, different materials for the solid matrix were used: aluminum, copper, brass, and titanium, respectively. The results obtained for the HDPE and iron particle showed good agreement between the models. These results also showed that the proposed model works well for frequencies up to 5MHz, which corresponds to the size parameter in the Rayleigh limit. It has been found that the acoustic properties of the solid matrix material strongly influence the results, and these may be useful in characterizing composite materials, containing inclusions and may also assist the development of implanted devices.