Summary
The paper presents a study of time-harmonic vibration of a half-space possessing a shear modulus linearly increasing with depth. Completing the previous paper [1], where the time-harmonic vibration of an incompressible half-space has been considered, the problem is now solved for a compressible as well as 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. The results show that, as compared to the homogeneous case, non-homogeneity can considerably increase vibration amplitudes at large distances from the applied force.
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Received 19 August 1996; accepted for publication 16, December 1996
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Muravskii, G. Green functions for a compressible linearly non homogeneous half-space. Archive of Applied Mechanics 67, 521–534 (1997). https://doi.org/10.1007/s004190050136
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DOI: https://doi.org/10.1007/s004190050136