Русская версия English version

Numerical research into parametric vibrations of pipeline in сase of pulsating liquid flows

B.A. Khudayarov

Vestnik IGEU, 2016 issue 5, pp. 54—59

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Abstract in English: 

Background: The widespread use of new composite materials at nuclear power facilities, in aircraft, oil and gas industries, at chemical production facilities, as well as other branches of engineering requires further improvement of mechanical models of deformable bodies and the development of methods and techniques of their calculation taking account of the viscoelastic properties of thin-walled structures material. Under these conditions, mathematical modeling of dynamic processes of pipelines with gas-liquid becomes especially important.

Materials and Methods: The pipeline deformation processes are described by using the integrated model of the Boltzmann-Volterra with weakly-singular hereditary kernels. With the help of the Bubnov-Galerkin method the mathematical model of the problem is reduced to the study of a system of ordinary integro-differential equations, where the independent variable is time. The solution to the integral-differential equations (IDE) is found by a numerical method based on elimination of singularity in the relaxation kernel of the integral operator.

Results: A mathematical model has been built to describe the problem of parametric vibrations of large viscoelastic pipelines with pulsating fluid flows. A computational algorithm has been developed based on elimination of singularity of integral and integro-differential equations with singular kernels, and subsequent use of quadrature formulas to solve the problems of dynamics of viscoelastic pipelines with pulsating fluid flows. The author has also investigated the influence of singularity in hereditary kernels and the excitation frequency on vibrations of structures with viscoelastic properties.

Conclusions: The account of viscoelastic properties of material structures reduces the amplitude and the oscillation frequency by 20–40 %. Increasing the excitation value depending on compressor workstation technology raises the amplitude and frequency of pipeline oscillation.

Key words: mathematical model, parametric oscillations, integro-differential equations, pipeline, viscoelasticity, nonlinear vibrations, numerical method.

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Ключевые слова на русском языке: 
математическая модель, параметрические колебания, интегро-дифференциальные уравнения, трубопровод, вязкоупругость, нелинейные колебания, численный метод
Ключевые слова на английском языке: 
mathematical model, parametric oscillations, integro-differential equations, pipeline, viscoelasticity, nonlinear vibrations, numerical method
The DOI index: 
10.17588/2072-2672.2016.5.054-059
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