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Group transformation method and ramification of solutions in twopoint boundary value problems of aeroelasticity, Differentsial'nye uravneniya i ikh prilozheniya: mater. mezhdunar. konf
T. Badokina, B. Loginov (2015)
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Green functions construction for divergence problems in aeroelasticity
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Matematicheskoe modelirovanie v zadachakh staticheskoi neustoichivosti uprugikh elementov konstruktsii pri aerogidrodinamicheskom vozdeistvii (Mathematical Modeling in the Problems of Static Instability of Elastic Elements of Constructions under Aerohydrodynamic Loads)
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Stability of a pipeline section with an elastic supportMechanics of Solids, 44
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P.A. Vel’misov, B.V. Loginov (1995)
Group transformation method and ramification of solutions in twopoint boundary value problems of aeroelasticity, Differentsial’nye uravneniya i ikh prilozheniya: mater. mezhdunar. konf., 20–22 dekabrya 1994 (Differ. Equations: Proc. Int. Conf., December 20–22, 1994)
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Instabilities and catastrophes in science and engineering
Applying bifurcation theory methods to nonlinear boundary value problems for ordinary differential equations (ODEs) of the fourth and higher orders encounters technical difficulties related to studying the spectrum of direct and adjoint linearized problems and constructing Green functions (i.e., proving the spectral problems to be Fredholm and determining the manifolds of bifurcation points). In order to overcome these difficulties, methods for separating the roots of relevant characteristic equations have been proposed, with the subsequent representation of the bifurcation manifolds in terms of these roots; this enables investigation of nonlinear problems in their rigorous statement. Such an approach is considered using the example of a two-point boundary value problem for a fourth-order ODE in which a statically bent pipeline section is described as a flexible elastic hollow rod, with a liquid flowing inside it, that is compressed or stretched by external boundary conditions with a free sliding left end and fixedly mounted right ends.
Differential Equations – Springer Journals
Published: Apr 20, 2018
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