Green functions for a compressible linearly non homogeneous half-space (Q1390114)

We study time-harmonic vibrations of a half-space possessing a shear modulus linearly increasing with depth. The problem is solved for a compressible as well as for an incompressible material. The half-space is subjected to a vertical or horizontal surface load. The solution is represented in terms of Fourier-Bessel integrals containing functions of depth coordinate that are expressed through confluent hypergeometric functions. Numerical results concerning surface displacements due to a point force are given for a wide range of frequency variations and degree of non-homogeneity.