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- W1967543238 abstract "A mathematical model for the non-linear stability of two-dimensional leakage channels is formulated and analyzed. It consists of an infinite channel with flexible elastic walls containing a flowing viscous, incompressible fluid. Two infinite elastic plates are inserted into the channel, parallel to the walls, to form parallel channels. The walls and the parallel plates are modeled by the Von Karman non-linear plate theory. To simplify the analysis, the fluid viscosity is modeled by Darcy's law rather than the Navier—Stokes law. Plug flow, where the fluid velocity is constant in each channel and the deflection of each wall is constant, is a solution of the problem for all values of the flow speed. The stability of the plug flow state is tested by the linearized stability theory. Stability is lost either by divergence or by flutter. The critical value of the flow speed depends on the system parameters and the mode of oscillation, either symmetric or antisymmetric. The non-linear problem is solved by the Poincare—Linstedt method near the critical flow speed for flutter. One or more branches of flutter solutions bifurcate from this critical speed depending on the multiplicity of the critical speed. It is shown, depending on the ranges of the system parameters, that the bifurcation is either supercritical or subcritical and that the supercritical (subcritical) solutions are stable (unstable). Finally, it is shown that secondary bifurcation of flutter states may occur depending on the values of the system parameter. In addition, “mode jumping” between flutter states may occur via the secondary bifurcation states, which are then quasi-periodic solutions of the non-linear problem." @default.
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- W1967543238 date "1993-02-01" @default.
- W1967543238 modified "2023-09-23" @default.
- W1967543238 title "Primary and secondary flutter of leakage flow channels" @default.
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- W1967543238 doi "https://doi.org/10.1016/0022-460x(93)90325-6" @default.
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