Breslavskyi I. Nonlinear normal modes in solutions of the vibration problems of thin shallow shells

The object of investigations are thin shallow shells of arbitrary shape in plan and constant and variable thickness. The goal of investigations is the development of an integrated approach, based on the nonlinear normal modes method, which allows analyzing free and forced nonlinear multimode vibrations of thin shallow shells and studying nonlinear dynamic processes of deformation, stability and bifurcations. Methods: analytical and numerical methods of the applied vibration theory: asymptotic methods, nonlinear normal modes method, harmonic balance method, Hill determinants method and Ince algebraization. Theoretical and practical results: new laws of nonlinear oscillations of shallow shells with complex geometry, including models of turbomachinery blades, were obtained. Originality consists in the development of the integrated nonlinear normal modes-based approach for the analysis of multimode nonlinear dynamics of thin shallow shells of arbitrary shape in plan under geometrically nonlinear deformation. Degree of implementation: research results, conclusions and recommendations are used in the practice of designing turbine blades in Open Stock Company "Turboatom". The branch of using: education, machine building.