THE PECULIARITIES OF THE FORMATION OF CONTACT INTERACTIONS IN A COMPOSITE SOLID UNDER FORCED OSCILLATIONS

The concept of rating dynamic statesis proposed in mechanical oscillatory systems created by the interactions of articulated elements. It is assumed that in real constructive solutions elastic, dissipative and mass-inertial elements are not always connected by kinematic pairs providing retaining or two-sided ties. Such situations are typical for many transport and technological vibration machines. The purpose of the article is to develop and detail a method for constructing mathematical models of the interaction of typical elements (or links) of mechanical oscillatory systems in order to determine the resulting coupling reactions in dynamic compounds. Methods of achieving the goal are based on the use of technology and methods of structural mathematical modeling, when the equivalent automatic control system is compared in a dynamic relation. A technology has been developed for the transformation of structural models, which allows for characteristic contact points to form dynamic coupling reactions, as the product of the system’s dynamic stiffness at a certain point and its dynamic displacement. The concepts of transfer functions of systems are used. It is shown that dynamic reactions at certain points of the system are fractional rational expressions, the values of which can vary widely depending on the frequencies of the external disturbance. Zero values of the coupling reactions determine the regimes in which the “rupture” of the kinematic coupling is possible. In the presence or accounting of standing forces, the limiting state is reached under conditions that take into account the effect of an additional force factor. The authors propose the introduction of the concept of the relationship of dynamic reactions at various points in the system, which forms certain information spaces. Methods and techniques for estimating dynamic states in compounds of system elements in problems of estimating a possible spectrum of expected dynamic states are proposed.

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