Natural Vibrations of a Liquid-Transporting Pipeline on an Elastic Base

Flexural free vibrations of an ideal-liquid-transporting pipeline on an elastic base are studied. A numerical-analytical method for finding the pipeline natural frequencies and vibration modes is developed, which permits one to determine the natural frequencies and modes for the case in which the tension or compression (the longitudinal force acting along the pipeline axis), the pipe diameter, and hence the velocity of the incompressible fluid being transported are arbitrary functions of the longitudinal coordinate measured along the pipeline axis. The least natural frequencies are calculated for the case in which the variable elasticity of the base is given by some test functions.