MATHEMATICAL MODELLING OF PROBLEM ON NON-LINEAR FLUTTER OF VISCO-ELASTIC SHELLS

In this work is investigated the flutter of viscoelastic cylindrical shell streamlined by gas current. The basic direction of work is consisted in taking into account of viscoelastic material’s properties at supersonic speeds. The vibration equations relatively of deflection are described by Integra-differential equations in partial derivatives. By Bubnov-Galerkin methods reduced the problems to investigation of system of ordinary Integro-Differential Equations (IDE). The IDE are solved by numerical method, which based on using of quadrature formula. The algorithm of the numerical solution on the basis of the method was described. Critical speeds for cylindrical shell flutter are defined. The influence of the viscoelastic property of the material, geometrical and aerodynamically non-linearity to the current value of critical speed and amplitude-frequency characteristics of the cylindrical shells was analyzed.