Discussion on the Time-Harmonic Elastodynamic Half-Space Green’s Function Obtained by Superposition

Abstract EN

The time-harmonic elastodynamic half-space Green’s function derived by Banerjee and Mamoon by way of superposition is discussed and examined against another semianalytical solution and a numerical solution.

It is shown that Banerjee and Mamoon’s solution gives infinite z-displacement response when the depth of the source goes to infinity, which is unreasonable and does not agree with other solutions.

A possible problem in the derivation is that it is inappropriate to directly extend the results of Mindlin’s superposition method for the elastostatic half-space problem to the dynamic case.

The superposition of the six full-space elastodynamic solutions does not satisfy the required boundary conditions of the half-space elastodynamic problem as in the static case and thus does not solve the dynamic half-space problem.