On the Mechanism of Energy Loss During Wave Propagation in an Elastic Medium Containing a Small Volume Fraction of Spherical Inclusions

Problems related to the identification of inhomogeneities, as well as the determination of their sizes and physical properties, are considered highly important and relevant in geophysics. This study investigates the influence of spherical wave curvature on the dynamic stresses in viscoelastic spherical bodies and the surrounding deformable medium. Based on the study of spherical compression wave scattering on a spherical body embedded in a viscoelastic medium, the dynamic stresses in both the body and the surrounding medium are determined. The aim of this study is to investigate the dynamic stress-strain state of spherical bodies under the action of spherical longitudinal or transverse harmonic waves, and to analyze the effect of spherical wave curvature on the dynamic stresses in viscoelastic spherical bodies. Methods. The equations of motion for spherical bodies are described by integro-differential equations derived based on the assumptions of viscoelasticity theory. The problem of diffraction of harmonic spherical waves in a spherical body is solved using displacement potentials. The displacement potentials are determined from the solutions of the Helmholtz equations. The arbitrary constants are found from boundary conditions imposed between the bodies. As a result, the formulated problem is reduced to a system of inhomogeneous algebraic equations with complex coefficients. Based on the methods of Muller, Gauss, and Laplace, a solution methodology and algorithm have been developed. Results In the course of the solution, it was found that at certain values of the viscoelastic and density parameters of the inclusion, low-frequency natural oscillations arise in the unbounded medium. These oscillations are essentially aperiodic motions, since the imaginary part of the natural frequency is large.