Numerical evaluation of integrals involving the product of two Bessel functions and a rational fraction arising in some elastodynamic problems

This paper presents numerical techniques for evaluating integrals of the form ∫0∞Jβ(kρ)Jγ(kR)kα(k−s)dk. These integrals arise during the application of the Hankel transform to pass the displacements of a layered soil profile from the wave number domain to the spatial domain in three-dimensional problems of elastodynamics. The objective here is to obtain solutions with an adequate accuracy from the engineering point of view to the integrals that arise in a first order formulation of a wave propagation model widely used for layered soils.