A Spectral Method Algorithm for Modeling the Dispersion of Non-Axisymmetric Modes in Fluid-Filled Elastic Tubes

Abstract

In order to design a low-noise water-filled pipeline system, it is necessary to obtain knowledge of the dispersion characteristics of axial propagation modes in different water-filled elastic tubes. In this work, an algorithm is developed based on the spectral method, which has previously been used to solve the dispersion of axisymmetric modes in cylindrical structures but has not yet been applied to non-axisymmetric modes. The algorithm can obtain the dispersion characteristics, modal displacement, and stress distribution of axial propagation modes in a fluid-filled elastic multi-layer tube. The algorithm behaves well both at low and ultrasonic frequencies, and it is suitable for any tube dimensions, wall thickness and layers. The results of a water-filled PMMA tube obtained using the spectral method algorithm were verified using a COMSOL simulation, while the dispersion curves of the same tube from the literature were found to be missing some low-order modes. In addition, the dispersion curves of a water-filled three-layer tube are given. The spectral method algorithm has the advantages of fast calculation speed, less computational resources consumed, accurate results, and no modal omission.