### Investigation of stability of viscoelastic element of construction in supersonic flow

#### A. V. Ankilov1, P. A. Velmisov2

Annotation The stability of deformable element in the form of a plate in the supersonic flow of ideal gas is investigated. Material aging, i.e. change of its physico-mechanical properties in the course of time, is taken into account. The model of aging viscoelastic body is applied where tension at any point depends on background of material’s deformation in this point, and connection between tension and deformation is described by Volterra-Feucht's equation. Aerodynamic pressure upon a plate is defined according to the piston’’ theory of A.A. Ilyushin. Based on the functional established in the paper the sufficient conditions for stability of the solution of partial integro-differential equation describing the plate dynamics are obtained. aeroelasticity, mathematical modeling, dynamical stability, plate, supersonic gas flow, differential equation, functional

1Associate professor of Higher Mathematics Department, Ulyanovsk State Technical University, Ulyanovsk; ankil@ulstu.ru

2Head of Higher Mathematics Department, Ulyanovsk State Technical University, Ulyanovsk; velmisov@ulstu.ru

Citation: A. V. Ankilov, P. A. Velmisov, "[Investigation of stability of viscoelastic element of construction in supersonic flow]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:3 (2016) 80–90 (In Russian)