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

3. The object of study: nonlinear oscillations and damping processes of beam elements of machines in the geometrically nonlinear deformation. Purpose of the study: to develop methods of analysis and suppression of nonlinear oscillations of beam elements of machines and manipulators in geometrically nonlinear deformation. Methods: Ostrogradskii-Hamilton, the method of Bubnov-Galerkin, method for nonlinear normal forms in combination with the method of multiple scales, the method of harmonic balance. Theoretical and practical results: the generalized nonlinear partial differential equations that describe the flexural-flexural-torsional vibrations of beams at their geometrically nonlinear deformation taking into account the warping of arbitrary cross-section were obtained. The possibility of damping the main subsystem with the help of Mises farm and two types of motions in nonlinear systems that implement an effective vibration damping were established. Scientific novelty: the first nonlinear normal forms in combination with the method of multiple scales were used to develop a method of analysis and research of nonlinear vibrations of beam elements of machines. Degree of implementation: an analysis of vibrations of helicopter blades used by the University of Michigan (USA, Ann Arbor), and methods of damping on the research and production enterprise "Khartron Arcos" (Kharkiv). The results of the thesis are used in the learning process in the Engineering Physics Department of NTU "KPI". Scope of application: aerospace, power engineering.