Forced vibrations of hereditary deformable shell elements of aircraft structures in gas flow under influence of atmospheric turbulence

Abstract

The problem of vibrations of thin, hereditarily deformable shell elements moving in a gas under the action of atmospheric turbulence is considered. The work aims to study the flutter phenomenon of aircraft elements in a gas flow under the action of loads caused by atmospheric turbulence. Assuming that the relationship between stresses and strains for the shell material is linear-hereditary, a thin shell is used, which obeys the Kirchhoff-Love hypothesis. The aerodynamic force is written according to the linearized piston theory. A system of nonlinear integro-differential equations in partial derivatives is obtained to describe nonlinear oscillations of a thin isotropic viscoelastic shell. The system of nonlinear integro-differential equations is solved numerically by the method proposed by F. Badalov, which is based on the Bubnov-Galerkin methods, finite differences, and power series. When using an exponential kernel, the flutter rate increases to approximately 1.5%. Therefore, when using an exponential kernel, the flutter velocity of a viscoelastic shell practically coincides with the critical flutter velocity for ideally elastic plates. It was also found that the critical flutter velocity increases with an increase in the number of pinched sides of the shell.