On the problem of some interface defect filled with a compressible fluid in a periodic stratified medium

A periodic two-layered elastic space containing an interface defect filled with a barotropic compressible fluid is considered. At infinity, the composite is subjected to a uniformly distributed load applied perpendicularly to the layering. Faces of the defect are under action of constant internal fluid pressure. An approximate solution to this problem is given within a certain homogenized model. The resulting singular integro-differential equation is obtained and solved for two types of defects by using an analogue of Dyson's theorem. The influence of the filler on the mechanical behaviour of the considered body is analysed and illustrated graphically.