Linear time heteronymous damping in nonlinear parametric systems

Basic research is a significant part of the dynamic analysis of complex planetary systems with kinematic couplings - gears. The high-speed light weakly and strongly non-linear parametric systems with minimum dimensions and masses are highly sensitive to the quality and quantity of their parameters. By influence of lightening holes in the discs of cogwheels, the damping in these systems can be time heteronymous. It reflects in the bifurcation characteristics of resonance courses of these systems and in their ambiguities. At the mass discretization, the analytical and numerical solution of these systems leads, to complicated systems of integro-differential equations with solving kernels in the form of Green´s resolventes and to complicated simulation models in MATLAB/Simulink. In terms of the internal dynamics, the special case of one transfer branch of split power flow of planetary system with six degrees of freedom will be analyzed in the study, i.e. the causation of quality and quantity of courses of bifurcation resonance characteristics and formation of ambiguity of characteristics of relative motions in gear meshes from view of influence of linear time heteronymous damping.