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TIME‐HARMONIC VIBRATION OF AN INCOMPRESSIBLE LINEARLY NON‐HOMOGENEOUS HALF‐SPACE
Author(s) -
MURAVSKII G.,
OPERSTEIN V.
Publication year - 1996
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/(sici)1096-9845(199611)25:11<1195::aid-eqe607>3.0.co;2-t
Subject(s) - half space , vibration , compressibility , mathematical analysis , dissipative system , mathematics , viscoelasticity , hankel transform , gravitational singularity , geometry , classical mechanics , physics , mechanics , acoustics , bessel function , quantum mechanics , thermodynamics
In this paper, time‐harmonic axisymmetric vibration of an incompressible viscoelastic half‐space having shear modulus linearly increasing with depth is studied. The half‐space is subjected to a vertical time‐harmonic load on its surface. Numerical results concerning surface displacements due to a point force are given for the case of non‐zero shear modulus at the surface. Hankel's transforms of the solutions have an infinite number of poles lying on the real axis of the complex plane in the non‐dissipative case. A suitable contour of integration is used to avoid all the singularities. Calculations are performed for the dynamic as well as for the static case. In addition, vertical vibrations of a rigid disk on the considered half‐space are investigated, and the influence of the non‐homogeneity on the dynamic stiffness of the loaded area is demonstrated.