β Scribed by A. O. Awojobi
No coin nor oath required. For personal study only.
The work presents an exact expression for the Hankel transform of the surface displacement of a rigid circular body performing harmonic vertical vibrations on a homogeneous elastic half-space of arbitrary Poisson's ratio interrupted at some depth by a frictionless horizontal plane. The Limiting case of the uninterrupted half-space is recovered in each of the extreme cases when the frictionless plane coincides with the surface or sinks to an infinite depth. Furthermore, the static case is derived in the limiting case of zero frequency and it is shown that the result agrees with the limiting case of zero gradient shear modulus variation for the static case of the incompressible non-homogeneous half-space.
It is also established that Poisson's ratio effect is linear, and the important proposition is again sustained that only surface shear modulus dominates vibrations on elastic media whereas any other factor such as the interruption of the frictionless plane as in the present case, merely constitutes a negligible secondary parameter.
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