Galas O. Development of methods of analysis and extinguishing of nonlinear vibrations of the bar systems

A research object is nonlinear dynamic deformation of bar constructions. The purpose of work is creation of models and methods of analysis and extinguishing of nonlinear vibrations of the bar systems. Ostrogradskogo-Gamil'tona method were used for the conclusion of equalizations of motion of the system; method of Bubnova- Galerkina for diskretization of vibrations and methods of the nonlinear normalized forms in combination with the method of multiple scales. As a result of the conducted work: nonlinear equations are first got in private derivatives of flexural-flexural-torsional vibrations of bar taking into account wrapping of transversal section. It was assumed at the conclusion of these equalizations, that centre of gravity and bend are in different points. The method of research of vibrations of the systems of large dimension is developed, combining the nonlinear normalized forms of Show- Pierre and method of multiple scales. The scientific novelty of the got results consists of that as a result of researches conducted in dissertation work the task of analysis geometrically of nonlinear spatial vibrations of the bar systems is decided taking into account wrapping of transversal section on condition that the centres of gravity and inflexibility of transversal section do not coincide. For the analysis of nonlinear vibrations of involute bars an analytical method which is based on sharing of method of the normalized forms and method of multiple scales was first offered. Drawn on the results of analysis of vibrations of blade of helicopter in the Michigan university (The USA, Ann Arbor), and methods of extinguishing of vibrations which are developed in dissertation, on the scientifically production enterprise of "Khartron-Arkos", Kharkov. Dissertation job performances are utillized in an educational process on the physical-engineering faculty of NTU "KhPI". The developed methods of calculation of nonlinear vibrations can be used for planning and polishing of elements of aerospace technique, power equipment and robototechnick systems.