Kushnir D. Stress state of multi-connected plates, covered by diaphragm

The thesis is devoted to research of three-dimensional concentration of the tension arising on surfaces of tunnel cavities in multiconnected plates, and also regularities of dynamic behavior of thick-walled and thin-walled cylinders under harmonious and pulse perturbations.The method of the solution of these tasks includes decomposition of functions in ranks on special system of homogeneous solutions, creation of the F-solutions, creation of integral representations of unknown functions, and also reduction of a boundary problem to system of the singular integrated equations.On the basis of analytical and numerical researches regularities in distribution of resonant frequencies of plates with openings and finite cylinders were revealed. The first resonant frequencies for cylinders of elliptic cross-section almost coincide at different ratios of half-axes, but essentially differ from those for the cylinder of circular cross-section.