Modeling the Deflection of Circular Membrane Effected by a Cargo Positioned Asymmetrically Relative to the Center
Abstract
The paper considers the problem of deflection of a circular membrane under the action of a load located at some distance from its center. The task consists in obtaining experimental data on the membrane deflection and constructing semi-empirical mathematical models based on a relatively small sample of experimental points to determine the magnitude of the deflection of the membrane at any given point on its surface. The deflection of the membrane, depending on the coordinate, can be described with acceptable accuracy by the Laplace equation. In the process of work, an exact solution of the Laplace equation was obtained using a method based on conformal mapping, and an approximate solution was obtained using the neural network modeling method. Calculations were carried out for cases of using two loads of different weights. As a result of the work, the distribution of the deflection of the membrane with known characteristics is obtained depending on the coordinate under the action of a load of a certain mass. In a method based on conformal mapping, the solution is a series. With an increase in the number of terms of the partial sum of the series approximating the solution, it becomes more accurate, but at the same time less resistant to errors introduced by experimental data. The neural network modeling method is more stable and leads to a solution that better agrees with the experiment. The difference between the calculated and experimental data is an order of magnitude smaller compared to the results obtained by the method based on conformal mapping.
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