The paper reviews approaches to defining free damped oscillation in mechanical drive of the technological equipment based on identifying the intrinsic oscillation frequencies given the Rayleigh dissipation function under non-linear dynamic effect. It presents a mathematical model for damped oscillation accounting for dissipative forces and their effect on the system vibration activity.
The paper is devoted to the consideration of the main reasons for the failure of various kinds of electromechanical instrument assemblies, caused by the occurrence of local defects in the material of the critical parts. The physical nature of the appearance of such defects, which is caused by discrete inclusions in the materials of parts, is disclosed. The origin of local defects largely affects the appearance of external vibration effects and dynamic processes in the nodes of the mechanisms of the devices and their further functioning and quality of work. A mathematical form of accounting for local defects when creating a mathematical model for describing a node of a mechanical system using Fourier analysis is given. The possible directions of development of local defects in the nodes of the system and the consequences of them are shown, and attention is also focused on the proposed methods for eliminating these defects in the manufacture of parts.
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