This article is cited in 2 papers

MECHANICS

Nonlinear flutter of the transient process of hereditarily deformable systems in supersonic flight mode

B. Sh. Usmonov^a, I. I. Safarov^a, M. Kh. Teshaev<sup>b

a</sup> Tashkent Institute of Chemical Technology, Tashkent, Uzbekistan
^b Bukhara Branch of the Institute of Mathematics of the Academy of Sciences of Uzbekistan, Bukhara, Uzbekistan

Abstract: In this paper, the problem of nonlinear flutter of a transient process of a hereditarily deformable wing of an aircraft moving at supersonic speed is considered. The aim of the work is to study the flutter problem for plate elements of aircraft in a gas flow under loads caused by atmospheric turbulence. Aerodynamic effects are specified according to the linearized piston theory. Nonlinear wing oscillations are described by a system of nonlinear integro-differential equations. They are solved numerically by the method proposed by F. Badalov, which is based on the Bubnov-Galerkin method, finite difference method, and power series. Free vibration is analyzed under conditions of ideal elasticity with account for a hereditarily deformable thin wing. The displacements of characteristic points of the wing under flutter conditions are comparatively assessed. It is established that aerodynamic nonlinearity has little impact on the critical speed, but with an increase in the Mach number, this impact increases. The mechanical effect of a significant dependence of the critical flutter speed on the relaxation kernel amplitude and Poisson's ratio is revealed.

Keywords: flexible plate, piston theory, flutter, aerodynamic impact, Bubnov-Galerkin method, relaxation kernel.

UDC: 534.1

Received: 03.04.2023
Accepted: April 10, 2024

DOI: 10.17223/19988621/88/10