Numerical solution of nonlinear problems in the filter of viscoelastic shells

The nutter of viscoelastic cylindrical shells streamlined by a gas current are investigated. The basic direction of the present work consists in taking into account of viscoelastic material properties at supersonic speeds. The vibration equations relative to deflections are described by integro partial differential equations. By the Bubnov–Galerkin methods, the problems are reduced to investigation of a system of ordinary integrodifferential equations (IDE). The IDEs are solved by a numerical method which is based on using the quadrature formulas. Critical speeds for the shell flutter are defined.