Mathematical modeling of the behavior of a plate in a wind tunnel

The paper presents two methods for constructing approximate solutions of the nonlinear problem of bending of an elastic thin rod shape under the influence of aerodynamic forces, they are the Hamiltonian approach and the representation of the solution in the form of a segment of the power series in the flow rate. The main idea of the first method consists in reducing the source of the Euler-Kirchhoff system to equations of Hamiltonian type with subsequent normalization of the Hamiltonian in a certain number of members (depending on the desired accuracy). In this approach, the search of the solution to the two-point boundary value problem is carried out by means of direct and inverse transformation of Birkhoff. The idea of the second approach is to write the equations of equilibrium for a change of the generalized coordinates and to represent the solution in the form of a segment of the power series in the free stream velocity. The results of both methods are compared.