Simulation of oscillations of composite pipelines conveying pulsating fluid

The article considers the problem of vibrations of straight sections of the pipeline based on the theory of beams. A mathematical model of the dynamics of a straight viscoelastic pipe with a pulsating fluid is developed. The speed of a pulsating fluid is assumed to be harmonically fluctuating and has the following form: V ( t ) = υ 0 (1 + μ 1 cosϖt ). The mathematical model of the problem is simplified using the Bubnov-Galerkin approach to the solution of a set of common integro-differential equations with time as an independent variable. A numerical approach based on the removal of the singularity in the relaxation kernel of the integral operator is used to solve integro-differential equations. A numerical approach for the unknowns was used to get the system of algebraic equations. The Gauss technique is used to resolve a set of algebraic equations. The dynamics of fluid-transporting viscoelastic pipes have difficulties that can be solved computationally.

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