Mathematical model of ultrasound transmission in gradient materials synthesized in arc surfacing under contact loading

The paper deals with a two-dimensional problem of time-dependent elasticitytheory, examining waves generated on the top layer interface by the source of normal stressesapplied to the top layer interface. Here the lower layer interface is free of stresses. The use is made of integral transformations to relate displacement transforms with stresses on the top layer interface. Exponent power series expansion is obtained for the transform of verticaldisplacements. Analytical approach to each member of the series ensures a precise solution of the problem. Displacement field vs. time dependence on the layer interface has been calculated. The findings are referred to in the process of ultrasound controlling t he layer by finite size sensors.