Propagation of low-frequency guided waves in three-dimensional submerged heterogeneous pipes.

Abstract

We numerically investigate the propagation of low‐frequency guided waves in a fluid‐filled elastic pipe submerged in a liquid. In a vacuum, axisymmetric modes travel through the pipe wall. When filled with a fluid of low sound speed, the pipe system can develop modes that are mainly supported by the interior fluid. As mode cut‐offs are approached, an increasing amount of energy penetrates the surrounding fluid. In order to determine these cut‐off frequencies, we have numerically obtained dispersion curves for the guided pipe modes from the characteristic equations for thick‐ or thin‐walled layered systems in cylindrical coordinates. As a complement to the separation of variable method, we also compute group speed curves from the propagation of interior source pulses through the medium using the time‐domain elastodynamic finite‐integration technique (EFIT). A time‐frequency analysis of the received signals at select probe locations reveals the group speed structure. We also compute the stability of the modes in the presence of heterogeneous contents such as gas or solid particulates using direct simulation with the EFIT code. Finally, we consider propagation through three‐dimensional structures such as valves.