Features of oscillating viscoelastic spherical bodies in a medium

The work examines the effect of harmonic waves on a spherical body. The problems of the eigenvalue of spherical bodies located in a viscoelastic medium are also studied. Numerical results were obtained for the stress-strain state of spherical bodies taking into account the rheological properties in the environment. Discrete eigenvalues of spherical bodies located in a viscoelastic medium were discovered.A mathematical formulation, solution method, algorithm and programs are proposed for determining complex natural frequencies and vibration modes in the problem of spherical bodies located in a viscoelastic medium, taking into account the rheological parameters of the mechanical system.