Axisymmetric Body-Force Fields in Elastodynamics of Transversely Isotropic Media

Abstract

In this paper, a complete elastodynamic solution for axisymmetric problems under axial body-forces in terms of two retarded potential functions in transversely isotropic media is extended to the case of general torsionless axisymmetry. Allowing for both axial and radial distributed internal loads through the use of an extra potential, the new solution retains its completeness via the theory of repeated wave equations. By virtue of its analytical design, the formulation can be reduced to the corresponding elastostatic case by simply suppressing the time-dependence of its potentials as well as the case of isotropy. In the limiting case of the latter material condition, the proposed representation for elastostatic problem degenerates to a recent extension of Love’s potential function.