Improper integrals for infinite elements in vibration of half spaces

In vibration of elastic and viscoelastic multilayered half spaces, the far field of each half space is discretized into infinite elements. Far-field displacement functions of three fundamental problems are used as the shape functions of appropriate infinite element nodal lines. Each fundamental problem solution is obtained as a linear combination of discrete waves. As a result, the mass and stiffness matrices of infinite elements involve improper integrals, which are evaluated by three schemes proposed herein. Different schemes are good for different ranges of the complex argument of the integrals.