Дослідження систем з електродинамічним та пружним зв’язком під час гармонійного збудження

Abstract

Abstract Purpose of the study is to analyze the operation of a mechanical system with the introduction of electrodynamic and elastic components into it to ensure that the operating modes of the latter go beyond the resonance modes. The tasks of the research involve the synthesis of the mathematical apparatus with the subsequent formation and analysis of the amplitude-frequency characteristics of the specified system. Research methods. The methodological basis of the work is the generalization and analysis of the known scientific results of the dynamics of systems in resonance modes and the use of a systematic approach. The analytical method and comparative analysis were used to form a scientific problem, form a goal and formulate research objectives. When creating empirical models, the main provisions of the dynamics of systems were used. The results of the study. Considering that the dynamic properties of the system depend on the presence or absence of an elastic connection of the transmission line, a combined system was subjected to research. Since it is impossible to obtain an exact analytical solution of the obtained system of nonlinear differential equations, the solution was carried out on an electronic model with harmonic excitation. Based on the results of studies on an electronic model, using the MatLab computer modeling system, it is difficult to establish the influence of the ratio of various parameters, with their possible variations in a large range, on the behavior of the system itself, since a question posed in this way will require a significant amount of computer time. Therefore, a study of the system with harmonious excitation in its linearized form was carried out. Conclusions. A mathematical model of the functioning of a system with electrodynamic and elastic coupling under harmonious excitation has been formed. On the basis of the research carried out, the amplitude-frequency characteristic of the system was built, with the help of which the correspondence of the results of the solution of the electronic (reference), built on the basis of MatLab, and the analytical models was established.