Numerical modeling of vibrations of viscoelastic pipelines conveying two-phase slug flow

A mathematical model of vibrations of horizontal viscoelastic pipelines conveying two-phase medium in a slug flow taking into account the internal pressure is proposed in the paper. In the study on vibrations of the pipeline conveying gas-containing fluid, a viscoelastic model of the theory of beams is used. The hereditary Boltzmann–Volterra theory of viscoelasticity with weakly singular hereditary kernels is used to describe the viscoelastic properties of the pipeline material. By means of the Bubnov–Galerkin method, the equations of the pipeline motion are reduced to the study of a system of ordinary integro-differential equations (IDE) with variable coefficients relative to a time function. The solution to the IDE is obtained numerically using the quadrature formulas. The effect of both gas and fluid phase flow rates, tensile forces in a longitudinal direction of the pipeline, internal pressure parameters, singularity parameters in the hereditary kernels on the vibrations of the pipeline made of composite material are studied numerically. It is found that the critical velocity of the gas flow decreases with an increase in the pressure inside the pipeline.