Summary
Time-harmonic vibrations of an incompressible half-space having shear modulus linearly increasing with depth are studied. The half-space is subjected to a surface load which has vertical or hovizontal direction. The general solution of the time-harmonic, in the vertical direction nonhomogeneous problem is constructed for arbitrary angular distribution in the horizontal plane. Numerical results concerning surface displacements due to a point force are given for the case of nonzero shear modulus at the surface. These results show that nonhomogeneity can considerably increase amplitudes at large distances from the applied force.
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Muravskii, G. Green functions for an incompressible linearly nonhomogeneous half-space. Arch. Appl. Mech. 67, 81–95 (1996). https://doi.org/10.1007/BF00787142
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DOI: https://doi.org/10.1007/BF00787142