System analysis in the assessment of the dynamic states of technical objects: dynamic vibration damping, connectivity of external excitations

Abstract

The scientific and methodological foundations of up-to-date machine dynamics are being developed within the framework of system analysis and methods of structural mathematical modeling. The goal is to develop methods for evaluating, monitoring, and forming dynamic states of objects that operate under vibration loads. The methods of mechanics are used to study mechanical oscillatory systems, which are considered as design schemes of technical objects of technological and transport purposes. Mathematical models are built on the basis of Lagrange equations of the second kind, Laplace integral transformations, and the possibilities of structural mathematical modeling. The technology of constructing mathematical models that allow using the possibilities of implementing dynamic vibration damping modes in systems is developed. A method for estimating the dynamic states in the modes of dynamic vibration damping in systems with two degrees of freedom under the action of two external forces acting together is developed. The results reflect the features of the dynamic damping modes, the dependence on the connectivity parameters of external harmonic perturbations. The results of numerical simulations are presented.