Positions of elastic equilibrium of a pipeline with vibrating supports

The spatial vibrations of a pipeline on two supports vibrating in the vertical direction with equal amplitudes and phases are considered. The pipeline movement consists of rotation (rolling) around a straight line passing through the supports and bending deformation. It is assumed that the bending occurs in the rolling plane without torsional deformation. Nonlinear equations of bending and angular motion of the pipeline are used. The pipeline movement was studied in the case where the bending is much more influenced by the internal pressure of the medium in the pipe than by its weight. The ranges of input parameters in which the upper and lower bent states of the pipeline are stable are determined by analogy with the Kapitza pendulum. Numerical calculations were carried out for a reinforced magnesium tube filled with methane.