Spatial Oscillations of a Pipeline with Vibrating Supports

Spatial oscillations of a section of a pipeline with a liquid contained in it during the translational vibrational movements of the supports are investigated. Oscillations of both supports occur with equal amplitudes, frequencies and phases. Pipe deformations associated with the exit of its axis from the bending plane are assumed to be small. The interactions of internal constant pressure and changes in the curvature of the axial line, longitudinal and circumferential deformations of the pipe are taken into account. Its flexural-rotational vibrations are described by a system of two non-linear differential equations. By applying the Bubnov–Galerkin method, this system is reduced to the Cauchy problem, which is then solved numerically by the Runge–Kutta method. In the case of small bending and angular motions of the pipe, a comparison of the analytical and numerical solutions is given. An analysis is given of periodic and non-periodic oscillations of steel, titanium and composite pipes, for which, in particular, frequency spectra and Poincare mappings are constructed.