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Generalized Abel transform for the analysis of fluid vibration in a tube

机译：Generalized Abel transform for the analysis of fluid vibration in a tube

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Fluid vibrations in axisymmetric geometry according to thefirst harmonic in the circumferential direction are analyzed. This problem has a practical application in the analysis of transverse vibrations of fluid in an axisymmetric pipe. The numerical model is developed using finiteelement techniques in axisymmetric geometry. Irrotational motions of ideal compressible fluid are analyzed. The finite-element model of the system is based on the approximation of nodal displacements via the shape functions. Thus the field of the amplitudes of the circumferential variation of the volumetric strain is calculated, exploiting conjugate approximation techniques. Obtained volumetric strains are used for the numerical construction of the interference pattern of the vibrating fluid. For this purpose the Abel transform, which is usually exploited in axisymmetric problems, is generalized for problems with circumferential variation of displacements. The obtained interference patterns are used in hybrid experimental-numerical procedures and help to interpret experimental results.

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