SH waves across a column sandwiched in an inhomogeneous medium

Abstract

The propagation or love waves across a vertical column sandwiched in a medium of different properties has been studied, Three different models are considered: (i) an infinite column in a semi-infinite medium, (ii) a column in a layer resting over a rigid bottom and (iii) a column in a layer resting over a semi-infinite elastic medium in welded contact with it. In each case the elastic properties vary vertically but this variation is the same both inside outside the column. Frequency equations have, been obtained for the regions inside and outside the column and dispersion curves drawn. As expected the wave periods change as the waves pass into and out of the column .Displacements in these regions have been obtained and presented graphically for points in the free surface .Reflection and transmission coefficients for normal Incidence at vertical discontinuities have also been  obtained.