Self-oscillatory process of a viscoelastic elongated plate

The object of research. The self-oscillating process of a viscoelastic elongated plate moving in a stationary, supersonic gas flow is considered, taking into account geometric and aerodynamic nonlinearities. A mathematical model, technique, computational algorithm, and a personal computer calculation program for estimating the flutter of a viscoelastic elongated plate in a gas flow have been developed. Method. Using the Bubnov-Galerkin method, based on the polynomial approximation of deflections, the problem is reduced to solving a nonlinear integro-differential equation of the Volterra type with a singular relaxation kernel, which is solved by a numerical method based on the use of quadrature formulas, which eliminates the singularities in the relaxation kernel. Results. The results of linear and nonlinear flutter calculations are presented for various physical, mechanical, and geometric parameters of a viscoelastic elongated plate. As a result of the study, it was found that taking into account the geometric nonlinearity leads to an increase and taking into account the viscoelastic properties of the material to a decrease in the values of the critical speed, while the rheological parameters of viscosity A and singularity α have a significant impact on the values of the critical speed, and the influence of the third rheological parameter β is insignificant.