Computer simulation of oscillatory processes of viscoelastic elements of thin-walled structures in a gas flow

¹ Department of Higher Mathematics,Tashkent institute of irrigation and agricultural mechanization engineers, Tashkent, 100000, Uzbekistan
² Scientific and Innovation Center of Information and Communication, Tashkent, 100000, Uzbekistan

^* Corresponding author: bakht-flpo@yandex.ru

Abstract

Results of numerical investigation of dynamic behavior of deformed wing aircraft in a gas flow are presented in the paper. Vibrations with respect to deflections are described by a system of integro-differential equations in partial derivatives. Using the Bubnov-Galerkin method, the problem is reduced to a system of ordinary integro-differential equations, where time is an independent variable. The solutions of integro-differential equations are determined by a numerical method based on the use of quadrature formulas. Computational algorithms and a package of applied programs have been created to solve problems on nonlinear flutter of viscoelastic elements of an aircraft. The reliability of the solution of the problem is confirmed by comparison with known numerical and analytical results. The effect of different boundary conditions on critical flutter velocity is studied. Critical velocity and critical flutter time of viscoelastic plates are determined. It is shown that the singularity parameter α affects not only the vibrations of viscoelastic systems, but also critical time and critical flutter velocity. It is stated that consideration of viscoelastic properties of plate material leads to 40 60% decrease in critical flutter velocity.