Problem statement. Given the prospects of discrete-continuous high-frequency vibration machines, there is a need to accurately assess the energy efficiency of such equipment. Since dissipation is an integral part of the dynamic processes in oscillating systems, it is important to develop a methodology that adequately accounts for energy losses during oscillation of continuous sections. Purpose. It consists of creating a mathematical model that carefully considers dissipative processes occurring in continuum sections. Methodology. The schematic diagram of a discrete-continuous oscillatory system is presented. The factors that influence energy dissipation during forced oscillations of the continuous section over a wide frequency range are determined. A mathematical model of oscillations of a continuous section is proposed using the finite element method and the theory of Timoshenko beams, accounting for dissipative processes. Findings (results) and originality (novelty). A mathematical model of complex damping of continuous sections of vibrating machines is described for the first time, which takes into account hysteresis, modal, aerodynamic damping and damping in supports. Practical value. A methodology for determining the damping of continuous sections is proposed to accurately assess the energy efficiency of discrete-continuous oscillatory systems over a wide frequency range. Scopes of further investigations. Future research involves analyzing the energy efficiency and stability of discrete-continuous oscillating systems of vibrating machines in resonant modes of continuous sections.
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