Title | A refinement of the equation for the deflection of a circular membrane based on variable coefficients in the qualified Euler method |
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Authors | D. A. Tarkhov^{1}, P. I. Vasilyev^{1}, D. A. Semenova^{1}, I. A. Shishkina^{1}^{1}Peter the Great St. Petersburg Polytechnic University |

Annotation | The solution of the problem of the deflection of a loaded circular membrane is considered. Based on an analytical solution of the equations of the equilibrium condition and the experimentally obtained data, a semiempirical model is obtained. The dependence of the deflection of the membrane on the distance to the center is expressed. With the help of the qualified Euler method, an improvement of the model was developed, which more reliably expresses the dependence of the deflection of the membrane from the distance to the center. |

Keywords | qualified Euler method, circular membrane, Laplace operator, semiempirical method, study of the dependence of deflection on the radius |

Citation | Tarkhov D. A., Vasilyev P. I., Semenova D. A., Shishkina I. A. ''A refinement of the equation for the deflection of a circular membrane based on variable coefficients in the qualified Euler method '' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 177-180. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper24.pdf. - Date of access: 24.08.2019. |

**© SVMO, National Research Mordovia State University, 2019**

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