Plaksiy K. Mathematical modeling of nonlinear dissipative systems resonance dynamics

The object of the research is resonance dynamics of the nonlinear dissipative vibrating systems. The aim of the work is the improvement of nonlinear dissipative systems resonance dynamics mathematical modeling by generalizing of a numerical-analytical method, which is based on the derivation of the simplified mathematical models in the form of reduced systems. Research methods are the generalized reduced systems method, the multiple time scales method, numerical methods, mathematical apparatus of nonlinear normal modes. Developing of the new class of dissipative systems simplified mathematical models, generalization of the resonance dynamics modeling method and the concept by Kauderer and Rosenberg, and the discovery of the new nonlinear normal mode have a scientific and theoretical value for the nonlinear dissipative systems resonance dynamics modeling problem. Practical significance of the obtained results consists in fact that they can be used for numerical-analytical modeling of resonance dynamics of constructions, machines and devices, which have vibrating elements. The obtained results novelty consists in development, investigation and theoretical justification of the new class of nonlinear dissipative systems simplified mathematical models in the resonance vicinity, in generalization of the numerical-analytical method of resonance dynamics modeling on the base of the proposed class of mathematical models for dissipative autonomous and non-autonomous systems, in generalization of the nonlinear normal vibration modes concept by Kauderer and Rosenberg for dissipative systems, in obtaining of new results concerning nonlinear dissipative systems resonance behavior, and in discovery of new nonlinear normal vibration mode. The research results are introduced in educational process at the department of systems and processes computer modeling, NTU "KhPI".