Guided Wave Propagation in Tubular Section With Multi-Layered Viscoelastic Coating: Part II — Circumferential Waves

Propagating waves physically admissible in a tubular section are derived to establish their dispersion characteristics in response to the presence of multi-layered viscoelastic coatings. Shear and longitudinal waves along the circumferential direction were investigated. To characterize the hollow cylinder with coating layers, wave dispersion and attenuation are studied using the “global matrix” technique. Since each layer is considered to be perfectly bonded to each other, displacement and strain continuity are imposed as the interfacial boundary conditions. Viscoelastic coating materials such as bitumen and epoxy serve to improve pipeline reliability, but they also dampen and dissipate wave energy. The viscoelastic materials are studied as well. By replacing the real material constants with complex material constants in the characteristic equation, the impact of the viscoelastic coatings on wave dispersion is established. Bisection method is followed to find the real and complex roots of the three characteristic equations derived. Roots thus obtained are manipulated to allow the phase velocity and attenuation dispersion to be plotted against frequency. The dispersion of phase velocity and wave attenuation for coated pipes are evaluated against a baseline model which is the bare, uncoated tubing to establish the propagation characteristics of the guided shear and longitudinal waves in the presence of multiple coating layers.