Nonlinear supersonic flutter for the viscoelastic orthotropic cylindrical shells in supersonic flow

Abstract

On the example of an orthotropic shell, the problems of the dynamics of thin-walled structures under aerodynamic loading are studied, taking into account the viscoelastic properties of material and geometric nonlinearity. The aerodynamic pressure is determined using the AA. Ilyushin's piston theory. Equations of motion relative to displacements are described by a system of integro-differential equations in partial derivatives. Using the Bubnov–Galerkin method, based on the polynomial approximation of deflections, the problem is reduced to a system of ordinary integro-differential equations, where time is an independent variable. Solutions of integro-differential equations are determined by a numerical method based on the elimination of the singularity in the relaxation kernel of the integral operator. Computational algorithms and applied programs have been developed to solve the problems on the nonlinear flutter for viscoelastic elements of an aircraft. The critical flutter speed for the viscoelastic orthotropic cylindrical shells is determined. It is established that an account of viscoelastic properties of shell material leads to a decrease in the critical flutter.