CONSTRUCTION AND ANALYSIS OF COMPUTER MODELS OF RESONATORS OF CAPACITIES OF TECHNOLOGICAL DEVICES BY VISUAL MEANS OF PYTHON
DOI:
https://doi.org/10.31649/1999-9941-2021-50-1-105-114Keywords:
resonator, oscillations, amplitude, frequency, capacitanceAbstract
Annotation. The study of nonlinear oscillations and processes in apparatuses that occur under the influence of complex oscillations presents significant mathematical difficulties. The arising strong nonlinear oscillations can significantly intensify technological processes or cause the destruction of structural elements. Therefore, the problem of using the vibrational energy arising in technological devices naturally matured for a long time both for equipment designers and production technologists.
A computer model based on a differential equation for determining the frequencies and forms of bending vibrations of a tubular resonator is proposed. The use of the model makes it possible to visualize the modes and frequency of oscillations for a resonator in the form of a cylindrical part of a technological apparatus of any size. This takes into account the thickness of the walls, the outer and inner diameter of the vessel of the apparatus, and its length. The model takes into account the type of tank fastening with variation in the support stiffness.
A distinctive feature of the resulting model is that for the first time an approach was used to solve the differential equation of capacity not by obtaining a numerical solution, but an approach was used that includes obtaining an analytical expression for each waveform with subsequent visualization using Python.
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