System approach in a generalized assessment of the vibrational interactions’ dynamic features of the elements of transport and technological objects under coherent force loadings

Abstract

The methodology of structural mathematical modeling is being developed to solve the problems of the dynamics of technical objects under vibration loading by coherent effects of a force nature. The purpose of the study is to develop a methodological framework for assessing and controlling the set of dynamic features of a mechanical oscillatory system, taking into account the coefficient of connectivity of external force disturbances, viewed as a variable tuning parameter. Within the framework of the methodology of structural mathematical modeling of a mechanical oscillatory system used as a design scheme of a technical object, it is compared with a structural diagram of a dynamically equivalent automatic control system. To build estimates of dynamic features, methods of automatic control theory, Laplace integral transformations, and graph theory are used. Using the example of a mechanical oscillatory system with two degrees of freedom, an approach has been developed to assess the totality of generalized dynamic features represented by states and modes of interactions in the form of oriented graphs viewed as peculiar invariants persisting at certain frequency intervals of external force disturbances. It is shown that connectivity coefficient of external perturbations, considered as a variable parameter of the system, has the potential to influence the significant dynamic properties of a mechanical oscillatory system, which are integrally expressed by the number of dynamic features in the form of dynamic interaction modes, resonances and states of zeroing the oscillation amplitudes of object coordinates whose dynamic condition is to be evaluated.