Vibration calculation of pipeline systems with arbitrary branches by the hybrid energy transfer matrix method

Abstract

The transfer matrix method (TMM) is an analytical method for investigating the vibrations in many structures such as beams, pipes, sheets, and shells. For long-span pipeline systems conveying fluid, the vibration solution method based on the TMM suffers from numerical instability when calculating in high frequency. In this paper, the hybrid energy transfer matrix method (HETMM) is built to analyze the vibration of pipeline system while avoiding the numerical instability problem. It can be directly and easily derived from the proven TMM. The calculation matrix dimension and form do not change with subunits number. The calculation program hardly varies, and the calculation time is short. So, the trial calculation can be carried out with little to no cost to determine the appropriate subunits number.Planar branched pipes of arbitrary shapes are prevalent in pipeline systems. The HETMM for fluid-filled pipeline system with any branched pipes is proposed in this paper, too. A dominant chain of the pipeline system is selected, and the influence of branched pipes at the junction will be “absorbed” by the dominant chain. Several numerical examples are presented to illustrate the application and stability of the proposed method. Results from the present approach are validated by measured and numerical data. Finally, the first-order natural frequency of a double-branch pipeline system is optimized combining the HETMM and the complex method. Through these examples, it is shown that the HETMM is efficient, stable in high frequency and can be used to calculate and optimize branched pipes of any shape.