Numerical modeling of the flutter problem of viscoelastic elongated plate

Abstract

The oscillatory processes that arise in the elements of technical thin-walled objects moving in a supersonic gas flow are investigated in the article. It is assumed that a plate of thickness h is flown around on one side by a supersonic gas flow with an undisturbed velocity V. Aerodynamic pressure is taken into account, according to A.A. Ilyushin's piston theory. The equation of vibrations with respect to deflections is described by partial integro-differential equations. Using the Bubnov - Galerkin method, based on a polynomial approximation of deflections, the problem is reduced to the study of a system of ordinary integro-differential equations, where time is an independent variable. The influence of physical, mechanical and geometrical parameters, constant efforts in the middle surface, and rheological parameters on plate flutter are studied. The table shows the critical flutter velocity depending on the physical-mechanical and geometrical characteristics of the plate.