Ala’Iddin A. Multilinked Cylindrical Solids Harmonic Conditions on its Flat Edges

F-Function method has been developed in this work. Also its application to three-dimensional elastic problems about harmonic oscillations of the thick plates with holes and finite cylindrical bodies is investigated. F-solution matrixes have been built for a layer under the mixed boundary conditions on its faces in the case of symmetric and skew-symmetric deformation. Symmetric and skew-symmetric problems about thick plate and finite cylinder oscillations are obtained with the help of these matrixes. Mentioned problems have been reduced to one-dimensional systems of Fredholm type singular integral equations, and then to a systems of linear algebraic equations. Several new problems of a great practical interest for a thick plate with a hole and finite cylinder have been solved in the case of the penny-shape cross-section, elliptical and quadrate cross-sections of the hole or cylinder. Numerical investigations of stress concentration have been made, new patterns were explored such as influence of a hole cross-section in the thick plate and finite cylinder, plate thickness (cylinder length), Poisson coefficient and forcing frequency on the stress concentration in solids. In particular, from the numerical results one can conclude, that stress concentration nearby the big axis extremities of an elliptic-shape hole is much higher, than for a penny-shape hole; although it is even greater nearby the corner point of the quadrate-shape hole; in the case of finite cylinder the form of its surface influence greatly on the resonance frequencies spectrum. At small loading frequencies, stress concentration, as a rule, is higher for bigger values of than for smaller values. On the contrary, for some values of high frequencies, stress concentration is higher for a small values of , than for a high values. Poisson coefficient influence is much higher for cylinder, than for a layer with a hole. Amplitude-frequency characteristics grow with the increasing of the layer thickness. Investigation results of the disserta-tion work have both theoretical and practical interest. Suggested principles can be used for various engineer-ing problems solving.