Abstract
The effect of non-stationary external forces on the vibration of pipelines made of composite materials is investigated in the paper. A mathematical model of composite pipeline vibration is developed, considering the viscosity properties of the structure and pipeline base material, axial forces, internal pressure, resistance forces, and external disturbances. A mathematical model of viscoelastic pipelines conveying fluid under vibrations is constructed based on the Boltzmann-Volterra integral model. The mathematical model to study a pipeline is based on the Euler-Bernoulli beam theory. Considering the physicomechanical properties of the pipeline material, the mathematical model of the problems under consideration presents a system of integro-differential equations (IDE) in partial derivatives with corresponding initial and boundary conditions. The nonlinear partial differential equations, obtained using the Bubnov-Galerkin method under considered boundary conditions, are reduced to solving the system of ordinary integro-differential equations. A computational algorithm is developed based on eliminating features of integro-differential equations with weakly singular kernels, followed by using quadrature formulas.
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