Open AccessMathematical modeling parametric vibrations of the pipeline with pulsating fluid flow
Author(s) -
B.A. Khudayarov,
Ф.Ж. Тураев
Publication year - 2020
Publication title -
iop conference series. earth and environmental science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.179
H-Index - 26
eISSN - 1755-1307
pISSN - 1755-1315
DOI - 10.1088/1755-1315/614/1/012103
Subject(s) - mathematics , ordinary differential equation , relaxation (psychology) , kernel (algebra) , algebraic equation , differential equation , fluid dynamics , singularity , galerkin method , viscoelasticity , mathematical analysis , mechanics , physics , finite element method , nonlinear system , psychology , social psychology , combinatorics , quantum mechanics , thermodynamics
A mathematical model of the dynamics of a straight viscoelastic pipe conveying pulsating fluid has been developed in the paper. Using the Bubnov-Galerkin method, a mathematical model of the problem is reduced to solving a system of ordinary integro-differential equations, where time is an independent variable. Solution of integro-differential equations is determined by a numerical method based on the elimination of a singularity in the relaxation kernel of an integral operator. A system of algebraic equations is obtained according to the numerical method for unknowns. To solve the system of algebraic equations, the Gauss method is used. A computational algorithm is developed for solving the problems of the dynamics of viscoelastic pipelines conveying fluid.