Problem of Vibration Damping in Mechanical Systems: System Analysis, Modeling, Control

Abstract

System approaches are being developed in the problems of dynamics of transport and technological machines related to the provision of dynamic vibration damping modes and the identification of a number of specific effects characteristic of technical objects with working bodies representing solids. The methods of structural mathematical modeling are used, in which a mechanical oscillatory system, considered as a design scheme of a technical object, is compared with a structural scheme, equivalent in dynamic terms, of an automatic control system. It is shown that the modes of dynamic damping are realized through the fixation of fixed points called centers of rotation (or oscillations). A method is proposed for the analytical evaluation of the possibilities of forming dynamic states based on the use of generalized feedback transfer functions, coefficients of motion connectivity by coordinates, forms of dynamic interaction of system elements under the simultaneous action of two harmonic excitations. Within the framework of the interpretation under consideration, the key characteristic of a mechanical oscillatory system is the characteristic frequency equation and its transformations. The development of ideas about the form of dynamic interactions of elements of a mechanical oscillatory system is proposed. The concept of form generalizes ideas about the directions of change in time of the coordinate of a system element in relation to a change in an external force or kinematic excitation. The methodology for displaying a set of dynamic states and forms of dynamic interaction of elements of a mechanical oscillatory system based on oriented graphs is proposed.