A. V. Ankilov, P. A. Velmisov, G. A. Ankilov

Ulyanovsk State Technical University (Ulyanovsk, Russian Federation)

Abstract. The paper considers a linear differential operator and several nonlinear differential and integro-differential operators that form the basis to the equations of vibration of a deformable plate. In the nonlinear operators, the nonlinearity of the bending moment and of the damping forces, as well as the longitudinal force arising from the elongation of the plate due to its deformation are taken into account. Basing on the proposed equations, mathematical models of the mechanical system consisting of a non-deformable pipeline connected at one end with a sensor designed to measure the pressure in the combustion chamber of an aircraft engine and at the other end with this chamber have been developed. The sensitive element of the sensor, which transmits the pressure information, is a deformable plate, whose edges are rigidly fixed. The models take into account the aerohydrodynamic effect of the working medium on this element and the temperature variation over time along the thickness of the element. Using the small parameter method, the first approximation for asymptotic equations is obtained that describes joint dynamics of the working medium in the pipeline and of the sensitive element. The study of the elastic element’s dynamics is based on the application of the Bubnov-Galerkin method and on the numerical experiments in Mathematica 12.0. A comparative analysis of solutions for linear and nonlinear models is performed. The influence of the above-mentioned nonlinearity types on the change in the value of the plate deflection is shown.

Key Words: nonlinear partial differential equations, aero-hydroelasticity, pressure sensor, pipeline, elastic element, small parameter method, Bubnov-Galirkin method

For citation: A. V. Ankilov, P. A. Velmisov, G. A. Ankilov. Mathematical Modeling of the Pressure Measurement System in Aircraft Engines. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 26:3(2024), 294–312. DOI: https://doi.org/10.15507/2079-6900.26.202403.294-312

Information about the authors:

Andrey V. Ankilov, Ph. D. in Phys. and Math., Head of the Department, Department of Higher Mathematics, Ulyanovsk State Technical University (32 Severny Venets St., Ulyanovsk 430027, Russia), ORCID: http://orcid.org/0000-0002-5946-8535, ankil@ulstu.ru

Petr A. Velmisov, D. Sci. in Phys. and Math., Professor, Department of Higher Mathematics, Ulyanovsk State Technical University (32 Severny Venets St., Ulyanovsk 430027, Russia), ORCID: http://orcid.org/0000-0001-7825-7015, velmisov@ulstu.ru

Grigory A. Ankilov, Postgraduate Student, Department of Higher Mathematics, Ulyanovsk State Technical University (32 Severny Venets St., Ulyanovsk 430027, Russia), ORCID: http://orcid.org/0009-0006-6180-0652, ankilov1996@mail.ru