Methods of the theory of branching and catastrophes in the problem of divergence an elongated plate in a supersonic gas flow.
T. E. Badokina Yu. B. Rousak1
|Annotation||We consider the problem of computing the branching solutions of nonlinear eigen- value problem for an ordinary differential equation of the fourth order, describing the divergence of the elongated plate in a supersonic gas flow, compressible ( stretchable ) external boundary conditions and subjected to a small normal load. We construct the asymptotics of branching solutions in the form of convergent series in the small parameters. Fredholm property of the linearized spectral problem is proved by constructing the appropriate Green’s function, which for this type of tasks performed for the first time.|
|Keywords||buckling, aeroelasticity, bifurcation, branching equation.|
1Assistent, Mordovian State University after N.P. Ogarev, Saransk; firstname.lastname@example.org.
2Canberra University, Australia; email@example.com
Citation: T. E. Badokina Yu. B. Rousak, "[Methods of the theory of branching and catastrophes in the problem of divergence an elongated plate in a supersonic gas flow.]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,16:2 (2014) 26–35 (In Russian)