Oscillations of the Oil Pipeline Axis with Consideration of the Inertia Component When Pumping Diesel Fuel

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This study examines a single-span beam crossing without longitudinal deformation compensators during diesel fuel pumping. In addition to static forces, namely, the weight of the pipeline and the transported product, the analysis considers vertical components of inertial forces acting on the oil product and the pipeline itself. These forces are directed perpendicularly to the abscissa axis connecting the endpoints of the crossing. The inertial effects cause significant vertical oscillations of the pipeline, which have not been sufficiently addressed in previous research. This work aims to study these oscillations to determine the displacements of points along the pipeline axis, the magnitudes of the inertial forces, and the resulting bending moments at the crossing. A classical Fourier series method is applied to solve the formulated boundary value problem. The results show that oscillations occur in the vertical plane, are symmetrical relative to the center of the span, and are undamped. The maximum vertical displacement reaches approximately 57 mm at the midpoint of the crossing, and the oscillation period is around 0.415 s. Inertial force distribution and bending moments are also symmetric about the center. A detailed analysis with small time steps confirmed that the oscillations are strictly periodic, exhibiting equal displacements in the upward and downward directions. The results highlight that fatigue loads arise during the operation of such crossings, which is important for assessing the strength and stability of oil pipeline structures under real operating conditions.