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Phase Velocity And Attenuation Of Elastic Waves In Buried Pipes Filled With Viscous Fluid
Last modified: 2013-04-30
Abstract
Complex domain solution of the dispersion equation for a three-phase system consisting from an elastic liquid-filled pipe, embedded into elastic medium, is obtained and investigated. The studied waveguide supports propagating waves, characterized by dispersion and attenuation, influenced both by individual phase properties and structure interaction. Linearized balance equations for each phase are formulated within general 3-dimensional approach; their solutions for propagating axisymmetric mode are coupled at the interfaces by appropriate boundary conditions. Dynamic problem for the liquid phase was formulated with account for fluid viscosity. The dispersion equation was derived with the aid of Maple software and solved numerically. Phase velocity and wave attenuation were calculated for the system parameters corresponding to typical industrial 36² oil pipeline in soil, which was used in the measurements of pressure signal propagation. The results are presented in the form of frequency dependence of the group velocity and wave attenuation in the range ~ 100 – 1000 Hz; they were compared with experimental data, which were found to match generally well with theory.
References
1. R. Long, M. Lowe and P. Cawley, “Attenuation characteristics of the fundamental modes that propagate in buried iron water pipes”, Ultrasionics, 41, 509-519 (2003).
2.
K. Baik, J. Jiang, T. G. Leighton, “Acoustic attenuation, phase and group velocities in liquid-filled pipes”, J. Acoust. Soc. Am. 128 (5), November 2010.3.
V. N. R. Rao and J. K. Vandiver, “Acoustics of fluid-filled boreholes with pipe: Guided propagation and radiation”, J. Acoust. Soc. Am. 105, 3057-3066 (1999).4.
D. C. Gazis, Three-Dimensional Investigation of the Propagation of Waves in Hollow Circular Cylinders”, J. Acoust. Soc. Am, 31, 658-573 (1959).5.
P. Nagy and A. Nayfef, “Viscosity-induced attenuation of longitudinal guided waves in fluid-loaded rods”, J. Acoust. Soc. Am., 100, 1501-1508 (1996).