Vlasov O. Deformation of multilayered orthotropic structurally non-homogeneous shells under dynamic loads

This dissertation is devoted to the development of efficient methods solutions to problems of stress-strained state, free and forced vibrations, associated with dynamic processes in constructional non-homogeneous multilayered supported by the ribs of the shells with attached solid bodies. The shells stress-strained state, that takes their constructional non-homogeneity into consideration, has been studied on the base of thin elastic shells linear theory and Kirghof-Lyav’s hypothesis. The problem is solved by the Ritz method on the basis of the developed mathematical model. The vibration equations have been derived on the base of Lagrange’s variation principle for dynamical processes. The method of the shell system natural frequencies and mode shapes calculation has been developed using the Jacobi method. The main problem of the shells system stress-strained state is solved by the superposition principle. The results of the shells free vibration natural frequencies and their modes numerical investigation have been calculated. The forced vibration amplitudes and the stresses for the reinforced shells case, caused by the normal force, distributed by the harmonic law, are also given. Оbtained results of calculation have been analyzed for a wide range of the shells constructional, geometric and mechanical parameters. The dependences, characterizing the influence of the boundary conditions, stiffener ribs, attached solid bodies and material structural non-homogeneity on the shells system oscillation modes, frequencies and stress-strained state have also been received. The results of the research and developed mathematical models adequacy have been adopted by the comparison with the results of some well-known problems solution and experimental data.