Uniqueness of Solution and Well-Posedness of the Problem of Determining the Fastening Parameters of a Pipe Containing Flowing Fluid
A. M. Akhtyamov1,2, G. F. Safina3
1Bashkir State University, Ufa, 450076 Russia
2Mavlyutov Institute of Mechanics, Ufa Scientific Center, Russian Academy of Sciences, Ufa, 450054 Russia
3Bashkir State University, Neftekamsk, 452680 Russia
Keywords: труба с текущей в ней жидкостью, частоты колебаний, краевые условия, параметры упругого закрепления, задача диагностирования, единственность решения, компакт, pipe containing flowing fluid, vibration frequency, boundary conditions, elastic fastening parameters, diagnostics problem, uniqueness of solution, compact
Abstract
The inverse problem of determining the type and parameters of fastening of the pipe ends from the natural frequencies of the pipe flexural vibrations is formulated and solved for the case of fluid flowing through the pipe. The uniqueness of the solution of the problem is proved, and the Tikhonov well-posedness of the problem is shown. A method for solving the inverse problem is proposed, and examples of the solution are given.
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