Asymptotic solution of the problem of the action of a stamp on an elastic layer lying on the surface of a compressible fluid of infinite depth

V. P. Ryabchenko

Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090

Abstract: This paper considers a two-dimensional linear unsteady problem of rigid-stamp indentation on an elastic layer of finite thickness lying on the surface of a compressible fluid of infinite depth. The Lamé equations holds for the elastic layer, and the wave equation for the fluid velocity potential. Using the Laplace and Fourier transforms, the problem is reduced to determining the contact stresses under the stamp from the solution of an integral equation of the first kind, whose kernel has a logarithmic singularity. An asymptotic solution of the problem is constructed for large times of interaction.

Keywords: stamp, elastic layer, compressible fluid, contact stresses.

UDC: 532.591+539.3

Received: 22.12.2006
Accepted: 14.03.2007

 English version: Journal of Applied Mechanics and Technical Physics, 2008, 49:2, 267–276

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