Construction and analysis of computer models of resonators of capacitance of technological devices by visual means of python
Olga Oliynyk, Yuriy TaranenkoThe study of nonlinear oscillations and processes in devices under the influence of complex oscillations causes significant mathematical difficulties. Strong nonlinear oscillations can significantly intensify technological processes or cause the destruction of structural elements. Therefore, the problem of using the vibrational energy arising naturally in technological devices has been brewing for a long time both for equipment designers and production technologists.
A computer model based on a differential equation is proposed to determine the frequencies and shapes of bending vibrations of a tubular resonator. Application of the model makes it possible to visualise the shapes and frequency of vibrations for a resonator in the form of a cylindrical part of a technological apparatus of any size. The model takes into account the wall thickness, outer and inner diameters of the vessel, and its length. The model takes into account the type of tank mounting with variation of the support stiffness.
A distinctive feature of the model is that for the first time, an approach to solving the differential equation of the tank was used not by obtaining a numerical solution, but by obtaining an analytical expression for each form of oscillation with subsequent visualisation using Python