Geodesic
Mathematical modeling of some aeroelastic systems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 1, Tome 206 (2022), pp. 23-34.

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In this paper, we develop mathematical models of a class of aerohydroelastic systems, namely, vibrating devices intended for intensification of technological processes. The dynamic stability of elastic components of these devices is examined. The notion of stability of a deformable body accepted in this paper coincides with the concept of the Lyapunov stability of dynamical systems. The models considered are governed by coupled nonlinear partial differential systems. The impact of a gas or fluid (in the model of an ideal medium) is determined from the asymptotic equations of aerohydromechanics. For describing the dynamics of elastic elements, we use the nonlinear theory of solid deformable bodies, which takes into account transverse and longitudinal deformations. The study of stability is based on the construction of positive-definite Lyapunov-type functionals. Sufficient conditions for the stability of solutions of the systems proposed are obtained.
Keywords: aerohydroelasticity, mathematical modeling, dynamic stability, elastic plate, subsonic fluid flow, partial differential equations, functional. 
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P. A. Vel'misov; A. V. Ankilov. Mathematical modeling of some aeroelastic systems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Winter Mathematical School "Modern Methods of Function Theory and Related Problems", Voronezh, January 28 - February 2, 2021, Part 1, Tome 206 (2022), pp. 23-34. http://geodesic.mathdoc.fr/item/INTO_2022_206_a2/

[1] Ankilov A. V., Velmisov P. A., Funktsionaly Lyapunova v nekotorykh zadachakh aerogidrouprugosti, UlGTU, Ulyanovsk, 2019

[2] Ankilov A. V., Velmisov P. A., Funktsionaly Lyapunova v nekotorykh zadachakh dinamicheskoi ustoichivosti aerouprugikh konstruktsii, UlGTU, Ulyanovsk, 2015

[3] Bykova T. V., Mogilevich L. I., Popov V. S., Popova A. A., Chernenko A. V., “Radialnye i izgibnye kolebaniya krugloi trekhsloinoi plastiny, vzaimodeistvuyuschei s pulsiruyuschim sloem vyazkoi zhidkosti”, Tr. MAI., 110 (2020), 6

[4] Velmisov P. A., Ankilov A. V., Pokladova Yu. V., “Ob ustoichivosti reshenii nekotorykh klassov nachalno-kraevykh zadach v aerogidrouprugosti”, Itogi nauki i tekhn. Ser. Sovr. mat. prilozh. Temat. obz., 165 (2019), 34–46

[5] Kollatts L., Zadachi na sobstvennye znacheniya, Nauka, M., 1968

[6] Mogilevich L. I., Blinkov Yu. A., Ivanov S. V., “Volny deformatsii v dvukh soosnykh kubicheski nelineinykh tsilindricheskikh obolochkakh s vyazkoi zhidkostyu mezhdu nimi”, Izv. vuzov. Prikl. nelin. dinam., 28:4 (2020), 435–454

[7] 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”, Int. J. Nonlin. Mech., 118 (2020), 103290 | DOI | MR

[8] Ankilov A. V., Vel'misov P. A., “Stability of solutions to an aerohydroelasticity problem”, J. Math. Sci., 219:1 (2016), 14–26 | DOI | MR | Zbl

[9] Askari E., Jeong K.-H., Ahn K.-H., Amabili M., “A mathematical approach to study fluid-coupled vibration of eccentric annular plates”, J. Fluids Struct., 98 (2020), 103129 | DOI

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

[11] Kontzialis K., Moditis K., Paidoussis M. P., “Transient simulations of the fluid-structure interaction response of a partially confined pipe under axial flows in opposite directions”, J. Press. Vessel Techn., 139:3 (2017), 1–8 | DOI

[12] Moditis K., Paidoussis M., Ratigan J., “Dynamics of a partially confined, discharging, cantilever pipe with reverse external flow”, J. Fluids Struct., 63 (2016), 120–139 | DOI

[13] Mogilevich L., Ivanov S., “Waves in two coaxial elastic cubically nonlinear shells with structural damping and viscous fluid between them”, Symmetry., 12:3 (2020), 335 | DOI

[14] Mogilevich L. I., Popov V. S., Popova A. A., Christoforova A. V., “Hydroelastic response of a circular sandwich plate interacting with a liquid layer”, J. Phys. Conf. Ser., 1546:1 (2020), 012137 | DOI

[15] Rinaldi S., Paidoussis M. P., “An improved theoretical model for the dynamics of a free-clamped cylinder in axial flow”, J. Fluids Struct., 94 (2020), 102903. | DOI

[16] Velmisov P. A., Ankilov A. V., “Dynamic stability of plate interacting with viscous fluid”, Cybern. Phys., 6:4 (2017), 262–270

[17] Velmisov P. A., Ankilov A. V., “Stability of solutions of initial boundary-value problems of aerohydroelasticity”, J. Math. Sci., 233:6 (2018), 958–974 | DOI | MR | Zbl

[18] Velmisov P. A., Ankilov A. V., “About dynamic stability of deformable elements of vibration systems”, Cybern. Phys., 8:3 (2019), 175–184 | DOI