The Lambʹs problem for a half-space covered with the pre-stretched layer

The Lambʹs problem for the half-space covered with the pre-stretching layer is studied within the framework of the piecewise homogeneous body model. The three-dimensional linearized theory of elastic waves in initially stressed bodies is used. It is assumed that a time-harmonic point-located normal force acts on the free face plane of the covering layer. A numerical algorithm is also developed. Numerical results are presented for two cases of material pairs: rubber (layer)+aluminum (half-space); and aluminum (layer)+rubber (half-space). These results involve stresses acting on the interface plane and in the covering layer. The influence of the harmonic force frequency and the pre-stretching of the covering layer on the distribution of stresses is analyzed. In particular, it is established that stresses on the interface plane are decreased as the pre-stretching is increased.