Abstract
A study is made of the axisymmetric problem of wave propagation under the influence of gravity in a micropolar viscoelastic semi‐infinite medium when a time varying axisymmetric loading is applied on the surface of the medium. Special attention is given to the effects of gravity which induces a kind of initial stress of a hydrostatic nature on the wave propagation.
Highlights
In classical problems of wave propagation in an elastic medium studied by several authors including
FORMULATION OF TI-IE PROBLEM We consider a viscoelastic homogeneous isotropic centrosymmetric body and assume that the initial stress due to gravity is hydrostatic in nature Since the initial stress is hydrostatic, stress strain relations
On the free surface z 0, the axially symmetrical and time varying loadings normal and tangential to the boundary surface and moment with a vector tangent to a circle of radius r are applied The displacement components ur, u and rotation component wo are independent of 0 We introduce a scalar potential and a vector potential b and express the displacement components u,., Uz in terms of these potentials
Summary
Love and De and Sengupta [2], it has been shown that the velocity of Rayleigh waves increases by a significant amount when the wave-length is large due to the influence of gravity Biot [3] investigated the influence of gravity on Rayleigh waves under the assumption that the force of gravity generates an initial stress of a hydrostatic nature so that the medium remains incompressible Nowacki and Nowacki [4] discussed the axisymmetric Lamb’s problem in a semi-infinite micropolar elastic solid they did not include the effects of gravity in a micropolar viscoelastic solid medium The main purpose of this paper is to consider the axisymmetric Lamb’s problem in a semi-infinite micropolar viscoelastic medium under the influence of gravity due to a harmonically oscillating loading acting on the surface of the medium Special attention is given to the effects of gravity which generates an initial stress hydrostatic in nature, on the wave propagation. We use the cylindrical polar coordinates (r,O,z) Without body couples, external loading distributions, body forces, the displacement vector u, rotation vector w depend only on r, z and because of the axisymmetric configuration The equations of motion in a micropolar viscoelastic solid medium under the influence of gravity are given by
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