Email this article Nonlinear mathematical model of pressure measurement systems in gas-liquid media
- Authors: Velmisov P.A.1, Tamarova Y.A.1
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Affiliations:
- Ulyanovsk State Technical University
- Issue: Vol 25, No 4 (2023)
- Pages: 313-325
- Section: Applied mathematics and mechanics
- Submitted: 23.12.2025
- Accepted: 23.12.2025
- Published: 24.12.2025
- URL: https://journal-vniispk.ru/2079-6900/article/view/360887
- DOI: https://doi.org/10.15507/2079-6900.25.202304.313-325
- ID: 360887
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Abstract
The primary element of the instrumentation for measuring the pressure of a gas-liquid medium is a sensor that supplies data on the pressure of the working medium. It determines the proper functioning of machines, mechanisms, and systems. Increasing the service life, reducing development time, and reducing the cost of sensors is one of the important tasks. Mathematical modeling of pressure measurement systems’ functioning plays an important role at the design stage of such systems. This article examines a nonlinear one-dimensional model of a mechanical system “pipeline – pressure sensor” designed to measure and control the pressure of the working gas-liquid medium in the combustion chambers of engines. In such a system, the sensor is connected to the engine via a pipeline and is located at some distance from it to reduce the impact of vibration accelerations and high temperatures. The purpose of the work is to study the dynamics and stability of joint oscillations of the elastic sensitive element in the pressure sensor and of the working medium in the pipeline for a given law of pressure change in the combustion chamber. The study is provided under the assumption that the working medium is ideal and compressible. To describe the movement of the working medium (gas or liquid), a nonlinear model of fluid and gas mechanics is used. Mathematical description of the process of interest includes an initial boundary value problem, whose formulation contains a nonlinear partial differential equation. To solve it, numerical-analytical method of solution based on the Galerkin method is proposed, which makes it possible to reduce the study of the problem to solving a system of ordinary differential equations. A numerical experiment is carried out and examples of calculating the dynamics of the sensor's sensitive element are presented. The proposed mathematical model makes it possible to determine the law of change in the deviation of the sensor's sensitive element depending on the law of change in pressure in the combustion chamber. The research results are intended for use at the design stage of pressure measurement systems.
About the authors
Petr Alexandrovich Velmisov
Ulyanovsk State Technical University
Email: velmisov@ulstu.ru
ORCID iD: 0000-0001-7825-7015
SPIN-code: 3073-0889
Scopus Author ID: 6506739055
ResearcherId: D-5785-2017
Professor, Doctor of Physical and Mathematical Sciences, Professor of the Department of Higher Mathematics
Russia, 432027, Ulyanovsk, Severny Venetz Str., 32Yuliya A. Tamarova
Ulyanovsk State Technical University
Author for correspondence.
Email: kazakovaua@mail.ru
ORCID iD: 0000-0001-6408-1573
Postgraduate Student, Department of Higher Mathematics
Russian Federation, 32 Severny Venets St., Ulyanovsk 432027, RussiaReferences
- L.G. Etkin, [Vibration sensors. Theory and practice], MGTU im. N. E. Baumanaт Publ., Moscow, 2004 (In Russ.), 407 p.
- A.A Kazaryan, G.P Groshev, "[Universal pressure sensor]", Izmeritel’naya tekhnika, 3 (2008), 26–30 (In Russ.).
- J. Ash, et al., [Sensors of measuring systems: in 2 books.], Mir Publ., M., 1992 (In Russ.).
- D. I. Agejkin, E.N. Kostina, N.N. Kuznecova, [Sensors of control and regulation], N. Mashinostroyeniye Publ., Moscow, 1965 (In Russ.), 928 p.
- V.P. Korsunov, [Elastic sensitive elements], Saratov State Univ. Publ., Saratov, 1980 (In Russ.), 264 p.
- [Sensors. Converters. Systems: Catalog.], FGUP NII fizicheskikh izmereniy Publ., Penza, 2012 (In Russ.).
- V.M. Pankratov, V.E. Dzhashitov, V. I. Ulybin, E.A. Mokrov, V.A. Semenov, D.V. Tihomirov, "[Mathematical models of the functioning of a pressure sensor for spacecraft at non-stationary temperatures of the measured and environmental media]", Microsistemnaya tekhnika, 2003, no. 6, 20–29 (In Russ.).
- E.M. Belozubov, N.E. Belozubova, "[Increasing the resistance of thin-film nano- and microsystems and pressure sensors based on them to the effects of increased vibration accelerations]", Trudy Mezhdunarodnogo simpoziuma "Nadezhnost’ i kachestvo", 2011, no. 2, 426–429 (In Russ.).
- A.V. Ankilov, P.A. Velmisov, V.D. Gorbokonenko, Yu.V. Pokladova, [Mathematical modeling of the mechanical system "pipeline – pressure sensor"], UlGTU Publ., Ulyanovsk, 2008 (In Russ.), 188 p.
- P.A. Velmisov, Yu.V. Pokladova, [Study of the dynamics of deformable elements of some aerohydroelastic systems], UlGTU Publ., Ulyanovsk, 2018 (In Russ.), 152 p.
- P.A. Velmisov, Yu.V. Pokladova, E. S. Serebryannikova, "[Mathematical modeling of the system "pipeline – pressure sensor"]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva, 12:4 (2010), 85–93 (In Russ.).
- P.A. Velmisov, Yu.V. Pokladova, "Mathematical modelling of the "pipeline – pressure sensor" system", Journal of Physics: Conference Series, 1353 (2019) (In Russ.). DOI: https://doi.org/10.1088/1742-6596/1353/1/012085
- P.A. Velmisov, Yu.V. Pokladova, U. J. Mizher, "Mathematical modelling of the mechanical system "pipeline – pressure sensor" ", AIP Conference Proceedings, 2172 (2019) (In Russ.). DOI: https://doi.org/10.1063/1.5133495
- A. I. Zemlyanukhin, S.V. Ivanov, L. I.Mogilevich, V. S.Popov, A.YU. Blinkov, "[Mathematical model for studying nonlinear waves in an elastic cylindrical shell surrounded by an elastic medium]", Prikladnaya matematika i mekhanika, 2014, no. 10, 80–83 (In Russ.).
- Yu.A. Blinkov, E.V. Yevdokimova, L. I.Mogilevich, A.Yu.Rebrina, "[Modeling of wave processes in two coaxial shells filled with a viscous liquid and surrounded by an elastic medium]", Vestnik RUDN. Seriya MIF, 26:3 (2018), 203—215 (In Russ.). DOI: https://doi.org/10.22363/2312-9735-2018-26-3-203-215
- L. I. Mogilevich, D.V. Kondratov, T. S.Kondratova, S.V.Ivanov, "[Mathematical modeling of deformation waves in two coaxial, cubically nonlinear shells interacting with the environment and filled with liquid]", Matematicheskoye modelirovaniye, komp’yuternyy i naturnyy eksperiment v yestestvennykh naukakh, 4 (2020) (In Russ.).
- DOI: https://doi.org/10.24411/2541-9269-2020-00003
- P.A. Velmisov, YU.A. Tamarova, "[Mathematical modeling of pressure measurement systems in gas-liquid media]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva, 22:3 (2020), 352—367 (In Russ.). DOI: https://doi.org/10.15507/2079-6900.22.202003.352-367
- YU.A. Tamarova, P.A. Velmisov, N.D. Aleksanin, N. I. Nurullin, "[Study of dynamic processes in systems for measuring pressure of gas-liquid media]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva, 23:4 (2021), 461—471 (In Russ.).
- K. Fletcher, [Numerical methods based on the Galerkin method], Mir Publ., 1988, 353 p.
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