Propagation characteristics of low-frequency axisymmetric waves in fluid-filled pipes embedded in the viscoelastic medium

The propagation characteristics of the low-frequency axisymmetric waves in buried fluid-filled pipes are investigated theoretically,based on the Kennard thin-walled shell equations,the Helmholtz equation,and the Kelvin-Voigt linear viscoelastic model.Analytic expressions of the phase velocity are derived for both the fluid-dominated wave and the shell-compressed wave under lubricated contact,via considering the surrounding soil as a viscoelastic medium.The dispersion and attenuation curves of the two wave types are obtained and verified numerically.The ratio of the radial pipe wall displacements is analyzed,with particular emphasis on the effects of the thickness-to-radius ratio and the quality factor on the dispersion and attenuation characteristics of the fluid-dominated wave.The results show that the viscoelastic property has slight effects on the phase velocities of the two wave types,but it influences the attenuation severely.The fluid-dominated wave influences the radial pipe wall displacement significantly and is the primary carrier of leakage noise energy;its phase velocity increases as a function of the thickness-to-radius ratio while the attenuation decreases.It also shows that the dispersion and attenuation of the fluid-dominated wave decrease as a function of the quality factor.The work will provide insights and guidance for the leakage detection of buried fluid-filled pipes.