The flutter problem of a physically nonlinear viscoelastic rod in a gas stream is considered taking into account the nonlinear pressure dependences of the aerodynamic effect. The statement of the problem and the method of solving the flutter of a viscoelastic rod taking into account the physical and aerodynamic nonlinearities are given. A mathematical model of the problem is constructed. Using the Bubnov-Galerkin method, based on a polynomial approximation of deflections, the problem is reduced to solving a system of non-linear integro-differential equations of Volterra type. To solve the resulting system, with a weakly singular Koltunov-Rzhanitsyn kernel, a numerical method based on the use of quadrature formulas is used.
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