Title | Comparative analysis of some mathematical models of engine pressure measurement systems |
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Authors | A. V. Ankilov^{1}, P. A. Velmisov^{1}, G. A. Ankilov^{1}^{1}Ulyanovsk state technical university |

Annotation | The paper considers linear and nonlinear differential operators, on the basis of which the equations of vibration of a deformable plate are written down. The nonlinear operators are obtained by generalising the linear operator to the case of nonlinearities of bending moment, damping force and longitudinal force. Based on the proposed equations, mathematical models of a mechanical system consisting of a pipeline filled with a gas-liquid medium and coupled at one end to a sensor for measuring the pressure in the combustion chamber of an aircraft engine and at the other end to this chamber have been developed. The sensing element of the sensor, which transmits the pressure information, is a deformable plate, the ends of which are rigidly fixed. On the basis of the small parameter method, asymptotic equations describing the joint dynamics of the working medium in the pipeline and the deformable element of the sensor are obtained. The study of the dynamics of the elastic element is based on the application of the Bubnov-Galerkin method and numerical experiments in Mathematica 12.0. A comparative analysis of solutions for linear and nonlinear models is performed. The influence of the above-mentioned types of nonlinearities on the change in the value of the plate deflection is shown. |

Keywords | nonlinear partial differential equations, aero-hydroelasticity, pressure sensor, pipeline, elastic element, small parameter method, Bubnov-Galerkin method. |

Citation | Ankilov A. V., Velmisov P. A., Ankilov G. A. ''Comparative analysis of some mathematical models of engine pressure measurement systems'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 26-28, 2024). Saransk: SVMO Publ, 2024. - pp. 12-17. Available at: https://conf.svmo.ru/files/2024/papers/paper01.pdf. - Date of access: 12.11.2024. |

**© SVMO, National Research Mordovia State University, 2024**

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