Особенности системных представлений о динамике механических колебательных структур при несимметричных связях

Abstract

The paper is devoted to a new approach to the formation of the methodological basis of system analysis in application to problems of the dynamics of mechanical oscillatory systems taking into account the forces of viscous friction. A mechanical oscillatory system with two mass-inertia elements connected to the support surfaces and to each other by elastic-dissipative elements is considered. A method for estimating the free movements of a mechanical oscillatory system is developed based on the characteristics expressed in terms of the parameters of the lever connections between the partial blocks in the form of a gear ratio. Mathematical models are built on the basis of Lagrange formalism, algebraic methods, and the theory of functions of a complex variable. A matrix method is proposed for constructing frequency functions and damping functions for mechanical oscillatory systems with two degrees of freedom based on the ratio of the potential and kinetic energy of the system, taking into account the forces of viscous friction. For a mechanical system in which the connection of elements with a single reference surface is reset, a graphic analytic analysis of the extreme properties of the corresponding frequency functions and damping functions is performed. A topological approach is proposed.