Unsteady motions of spherical shells in a viscoelastic medium

This paper considers the unsteady motions of the spherical bodies immersed in a viscoelastic medium under the action of unsteady waves. The relation between stresses and strains complies with the hereditary Boltzmann–Voltaire integral. Using the integral Laplace transform, an exact solution of the equations of motion is obtained in the images. The integrand function in the images satisfies Jordan's lemma. Using the residue theorem, displacements and stresses are determined as the functions of time. An algorithm is developed, and a program is compiled in C++. The numerical results are obtained and analyzed. It is revealed that the kinematic factors, i.e. acceleration and velocity, of the spherical shell differ significantly from those of the viscoelastic medium. Under short-term exposure to waves (loads), the diagram of the stress-strain state changes: at all points of the shell, the maximum stresses and strains are significantly higher than average values, and the stress attains the maximum at the frontal point. Some differences are also found in the variation of time-displacement dependence for the spherical shell and surrounding viscoelastic medium.