Abstract: The dynamic response of an elastic half-space with a cylindrical
cavity in a circular cross-section is analyzed. The cavity is assumed to be
infinitely long, lying parallel to the plane-free surface of the medium at a
finite depth and subjected to a uniformly distributed harmonic pressure at the
inner surface. The problem considered is one of plain strain, in which it is
assumed that the geometry and material properties of the medium and the forcing
function are constant along the axis of the cavity. The equations of motion are
reduced to two wave equations in polar coordinates with the use of Helmholtz
potentials. The method of wave function expansion is used to construct the
displacement fields in terms of the potentials. The boundary conditions at the
surface of the cavity are satisfied exactly, and they are satisfied
approximately at the free surface of the half-space. Thus, the unknown
coefficients in the expansions are obtained from the treatment of boundary
conditions using a collocation least-square scheme. Numerical results, which
are presented in the figures, show that the wave number (i.e., the frequency)
and depth of the cavity significantly affect the displacement and stress.
