On the divergence stability loss of elongated plate in supersonic gas flow subjected to compressing or extending stresses
Buckling of a thin flexible elongated plate subjected to supersonic flow of a gas along the Ox-axis and compressed or extended by external boundary stresses at the edges x = 0 and x = 1 is investigated. This problem is described by a nonlinear ordinary differential equation in dimensionless variables with two bifurcation parameters one of which characterizes the compression (extension) of the plate orthogonally to Oy-axis and the other is the Mach number. Six types of boundary conditions are considered according to different fixing conditions of the edges x = 0 and x = 1. In the case of unsymmetrical boundary conditions four possible variants of them are considered. The Lyapounov-Schmidt method of bifurcation theory is applied. In a neighborhood of each point of bifurcation curve small solutions asymptotics in form of convergent series of two small parameters are computed. In comparison with our previous results the integral term is introduced in the nonlinear equation taking into account complementary forces in the middle surface of the buckled plate. The main difficulties have arisen in the investigation
of relevant two-parametric eigenvalue problems and were overcome with the aid of the bifurcation curves representation through the roots of the corresponding characteristic equation.
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