Title | Dynamic stability of deformable elements of aeroelastic structures |
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Authors | P. A. Velmisov^{1}, A. V. Ankilov^{1}, Y. V. Pokladova^{1}^{1}Ulyanovsk State Technical University |

Annotation | The stability of solutions of initial-boundary value problems for integrodifferential partial differential equations describing the dynamics of deformable elements of various structures interacting with a gas-liquid medium (streamlined by a fluid or gas flow) is investigated in this paper. The definitions of the stability of a deformable (viscoelastic, elastic) body adopted in the paper correspond to the concept of stability of dynamical systems by Lyapunov. The stability of the elements of aircraft, pipeline systems, vibrating devices under different ways of fixing elements under subsonic or supersonic flow around a compressible or incompressible medium is studied. The effect of gas or liquid (in the model of an ideal medium) is determined from the asymptotic linear equations of aerohydromechanics. To describe the dynamics of elastic elements, both linear and nonlinear theories of a solid deformed body are used. |

Keywords | aerohydroelasticity, mathematical modeling, dynamic stability, elastic plate, subsonic flow of gas, the differential equations in private derivatives, functional |

Citation | Velmisov P. A., Ankilov A. V., Pokladova Y. V. ''Dynamic stability of deformable elements of aeroelastic structures'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 16-20, 2018). Saransk: SVMO Publ, 2018. - pp. 134-141. Available at: http://conf.svmo.ru/files/2018/papers/paper43.pdf. - Date of access: 26.04.2019. |

**© SVMO, National Research Mordovia State University, 2019**

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