Geodesic
Mathematical modeling of pressure measurement systems in gas-liquid media
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 22 (2020) no. 3, pp. 352-367.

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The article discusses the initial-boundary value problems for systems of differential equations, which are mathematical models of the mechanical system "pipeline - pressure sensor", that is designed to measure pressure in gas-liquid media. On the basis of the proposed models, the joint dynamics of the pressure sensor sensitive element and of the working medium in the pipeline connecting the sensor to the combustion chamber of the engine is investigated. To describe the movement of the working medium, linear models of the mechanics of liquid and gas are used; to describe the dynamics of the sensitive element, both linear and nonlinear models of the mechanics of a solid deformable body are used. The solutions of stated initial-boundary value problems are carried out on the basis of the Galerkin method and the finite-difference method.
Keywords: differential equations, aeroelasticity, pipeline, pressure sensor, elastic element, dynamics, finite difference method, Galerkin method. 
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P. A. Vel'misov; J. А. Tamarova. Mathematical modeling of pressure measurement systems in gas-liquid media. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 22 (2020) no. 3, pp. 352-367. http://geodesic.mathdoc.fr/item/SVMO_2020_22_3_a6/

[1] E. M. Belozubov, V. A. Vasil'ev, A. I. Zapevalin, P. S. Chernov, “Designing the elastic elements of nano- and microelectromechanical systems”, Measuring technique, 1 (2011), 17–19 (In Russ.)

[2] L. G. Etkin, Vibration sensors. Theory and practice, Publishing House of Moscow State Technical University. N.E.Bauman, M., 2004, 408 pp. (In Russ.)

[3] J. Ash et al, Sensors of measuring systems, in 2 books, Translation from fr., v. 1, Mir, M., 1992, 480 pp. (In Russ.)

[4] J. Ash et al, Sensors of measuring systems, in 2 books, Translation from fr., v. 2, Mir, M., 1992, 424 pp. (In Russ.)

[5] D. I. Agejkin, E. N. Kostina, N. N. Kuznecova, Sensors of control and regulation, N. Mechanical Engineering, M., 1965, 928 pp. (In Russ.)

[6] V. P. Korsunov, Elastic sensitive elements, Publishing house of the Saratov University, Saratov, 1980, 264 pp. (In Russ.)

[7] S. P. Pirogov, Manometric tubular springs, Nedra, S.Petersburg, 2009, 276 pp. (In Russ.)

[8] L. E. Andreeva, Uprugie elementy priborov, 2-e izdanie, Mashinostroenie, M., 1981, 392 pp. (In Russ.)

[9] E. A. Mokrov, D. V. Lebedev, V. P. Bazaev, E. V. Efremov, I. A. Semina, P. A. Kolchin, “On the design and technological improvement of strain gauge thin-film pressure sensors”, Sensors and systems, 6 (2008), 2–7 (In Russ.)

[10] E. M. Belozubov, E. A. Mokrov, D. V. Tihomirov, “Minimizing the error of thin-film strain gauge pressure sensors when exposed to non-stationary temperature”, Sensors and Systems, 1 (2004), 26–29 (In Russ.)

[11] P. A. Velmisov, V. D. Gorbokonenko, “About one mathematical model of the “pipeline – pressure sensor” system”, Mathematical modeling and boundary value problems, proceedings of the Eleventh Interuniversity Conference, v. 2, 2001, 15–17 (In Russ.)

[12] P. A. Velmisov, L. V. Garnefska, V. D. Gorbokonenko, “An investigation of mathematical models “pipeline-pressure sensor””, Applications of Mathematics in Engineering and Economics, Proceedings of the XXVII Summer School, 2002, 542–548

[13] P. A. Velmisov, V. D. Gorbokonenko, Yu. A. Reshetnikov, “Mathematical modeling of the mechanical system “pipeline – pressure sensor”, Sensors and systems, 6(49) (2003), 12–15 (In Russ.)

[14] P. A. Velmisov, Yu. V. Pokladova, E. S. Serebryannikova, “Matematicheskoe modelirovanie sistemy «truboprovod – datchik davleniya»”, Zhurnal SVMO, 12:4 (2010), 85–93 (In Russ.)

[15] P. A. Velmisov, Yu. V. Pokladova, “Mathematical modelling of the “pipeline – pressure sensor” system”, Journal of Physics: Conference Series, 1353 (2019), 1–6 | DOI

[16] P. A. Velmisov, Yu. V. Pokladova, U. J. Mizher, “Mathematical modelling of the mechanical system “pipeline – pressure sensor””, AIP Conference Proceedings, 2172 (2019), 030006 | DOI

[17] A. V. Ankilov, P. A. Velmisov, V. D. Gorbokonenko, Yu. V. Pokladova, Mathematical modeling of the mechanical system “pipeline – pressure sensor”, UlGTU, Ulyanovsk, 2008, 188 pp. (In Russ.)

[18] P. A. Velmisov, Yu. V. Pokladova, Study of the dynamics of deformable elements of some aerohydroelastic systems, UlGTU, Ulyanovsk, 2018, 152 pp. (In Russ.)

[19] S. K. Godunov, V. S. Ryabenkij, Difference schemes (introduction to theory), The main edition of the physical and mathematical literature of the Nauka publishing house, M., 1977, 440 pp. (In Russ.) | MR

[20] N. N. Kalitkin, Numerical methods, The main edition of the physical and mathematical literature of the Nauka publishing house, M., 1978, 512 pp. (In Russ.) | MR