Bending Vibrations of a Pipeline on Elastic Supports with Moving Liquid

The natural bending vibrations of a pipeline are investigated. It is assumed that the parts of the pipeline on both sides of the sagging section have elastic supports. It is assumed that a constant longitudinal force acts along the neutral line. An incompressible liquid flows through the pipe with a constant average velocity. The effect of the internal pressure in the pipe on these vibrations is taken into account. The direct and inverse problems are solved. The speed parameter, the mass of liquid per unit length of the pipeline, and the dimensionless mass flow rate of liquid through the pipeline can be determined from two frequencies of bending vibrations.