Geodesic
Mathematical modeling of the pressure measurement system in aircraft engines
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 26 (2024) no. 3, pp. 294-312.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: nonlinear partial differential equations, aero-hydroelasticity, pressure sensor, pipeline, elastic element, small parameter method
Mots-clés : Bubnov-Galirkin method 
@article{SVMO_2024_26_3_a4,
     author = {A. V. Ankilov and P. A. Vel'misov and G. A. Ankilov},
     title = {Mathematical modeling of the pressure measurement system in aircraft engines},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {294--312},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2024_26_3_a4/}
}
TY  - JOUR
AU  - A. V. Ankilov
AU  - P. A. Vel'misov
AU  - G. A. Ankilov
TI  - Mathematical modeling of the pressure measurement system in aircraft engines
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2024
SP  - 294
EP  - 312
VL  - 26
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2024_26_3_a4/
LA  - ru
ID  - SVMO_2024_26_3_a4
ER  - 
%0 Journal Article
%A A. V. Ankilov
%A P. A. Vel'misov
%A G. A. Ankilov
%T Mathematical modeling of the pressure measurement system in aircraft engines
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2024
%P 294-312
%V 26
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2024_26_3_a4/
%G ru
%F SVMO_2024_26_3_a4
A. V. Ankilov; P. A. Vel'misov; G. A. Ankilov. Mathematical modeling of the pressure measurement system in aircraft engines. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 26 (2024) no. 3, pp. 294-312. http://geodesic.mathdoc.fr/item/SVMO_2024_26_3_a4/

[1] Giacobbi D. B., Semler C., Paidoussis M. P., “Dynamics of pipes conveying fluid of axially varying density”, Journal of Sound and Vibration, 473 (2020), 115202 | DOI

[2] Abdelbaki A. R., Paidoussis M. P., Misra A. K., “A nonlinear model for a hanging cantilevered pipe discharging fluid with a partially-confined external flow”, International Journal of Non-Linear Mechanics, 118 (2020), 103290 | DOI

[3] D. V. Kondratov, T. S. Kondratova, V. S. Popov, M. V. Popova, “Modeling hydroelastic response of the channel wall resting on a nonlinear elastic foundation”, Lecture Notes in Mechanical Engineering, 2023, 261-–270 | DOI

[4] Mogilevich L. I., Popova E. V., “Prodolnye volny v stenkakh koltsevogo kanala iz materiala s drobnoi nelineinostyu, zapolnennogo zhidkostyu”, Izvestiya Vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya dinamika, 31:3 (2023), 365-376 | DOI

[5] P. A. Velmisov, A. V. Ankilov, Yu. V. Pokladova, “On the stability of solutions of certain classes of initial-boundary-value problems in aerohydroelasticity”, Journal of Mathematical Sciences, 259:2 (2021), 296–308 | DOI | MR | Zbl

[6] A. G. Dmitrienko, S. A. Isakov, E. M. Belozubov, “Datchiki davleniya na osnove nano- i mikroelektromekhanicheskikh sistem dlya raketnoi i aviatsionnoi tekhniki”, Datchiki i sistemy, 160:9 (2012), 19–25

[7] V. Stuchebnikov, Yu. Vaskov, E. Savchenko, “Spetsialnye datchiki davleniya promyshlennoi gruppy «MIDA»”, Komponenty i tekhnologii, 238:5 (2021), 12–15

[8] S. P. Pirogov, D. A. Cherentsov, A. Yu. Chuba, N. N. Ustinov, “Simulation of forced oscillations of pressure monitoring devices”, International Journal of Engineering Trends and Technology, 70:2 (2022), 32–36 | DOI

[9] L. G. Etkin, Vibrochastotnye datchiki. Teoriya i praktika, M.: Izd-vo MGTU im. N.E. Baumana, 2004, 408 pp.

[10] Zh. Ash i dr., Datchiki izmeritelnykh sistem: v 2-kh kn., M.: Mir, 1992, 419 pp.

[11] P. A. Velmisov, Yu. A. Tamarova, “Nelineinaya matematicheskaya model sistem izmereniya davleniya v gazozhidkostnykh sredakh”, Zhurnal Srednevolzhskogo matematicheskogo obschestva, 25:4 (2023), 313–325 | DOI

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

[13] P. A. Velmisov, Yu. A. Tamarova, “Matematicheskoe modelirovanie dinamiki aerouprugoi sistemy «truboprovod – datchik davleniya»”, Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika, 2024, no. 2, 69–78 | DOI