### Investigation of dynamic of one aeroelastical system of <<tandem>> species.

#### A. V. Ankilov^{1}, P. A. Velmisov^{2}

Annotation | The article proposes a mathematical model of the dynamical system consisting of the n elastic plates of «tandem» species flowing along of the subsonic flow of gas (liquid). The aerohydrodynamic impact on the plates is determined from the asymptotic equations of motion of a liquid or gas in the model of an ideal incompressible environment. The behavior of the elastic material is described by a linear model. For solving problem, the approach based on the construction of the solutions of aerohydrodynamic part of the two-dimensional boundary-value problem for Laplace's equation by methods of complex analysis is used. While the aerohydrodynamic load (pressure of liquid or gas) is defined through the functions describing the unknown deformations of the plates. Under the substitution of the pressure expression in the equation of oscillations of the plates the solution of the problem is reduced to the study of systems of coupled integro-differential equations with partial derivatives for the deformations functions. On the basis of the Bubnov-Galerkin method a software product is created. This product allows to find the solution of system of equations and to produce the investigation of the dynamics of the plates system. The program may to build the oscillations graphics the based on which we can to discuss the amplitude and frequency of oscillations and to make conclusions about their stability. On the basis of the numerical experiment the dependences of the character of the oscillations of elastic plates are analyzed from the parameters of the mechanical system. |
---|---|

Keywords | aerohydroelastisity, dynamic, elastic plate, system of <<tandem>> species, deformation, flow along the plate, subsonic flow |

^{1}Assistant professor of Higher Mathematics Chair, Ulyanovsk State Technical University, Ulyanovsk; ankil@ulstu.ru.^{2}Head of Higher Mathematics Chair, Ulyanovsk State Technical University, Ulyanovsk; velmisov@ulstu.ru.

**Citation**: A. V. Ankilov, P. A. Velmisov, "[Investigation of dynamic of one aeroelastical system of <