Dispersion and Attenuation of Guided Waves in Tubular Section with Multi-Layered Viscoelastic Coating — Part II: Circumferential Wave Propagation

Abstract

In the second part of the study on guided wave motions in a hollow cylinder with epoxy layers, shear and longitudinal modes propagating in the circumferential direction are investigated. The corresponding dispersion and attenuation characteristic equations are derived by incorporating a complex, frequency-dependent constitutive law for the viscoelastic coating material. Continuous displacement boundary conditions are implemented to model perfect interfacial bonds between the tubular section and applied epoxy coatings. The presence of thin dissipative viscoelastic layers has profound impact on the propagation of both the circumferential shear and longitudinal waves. The number of admissible propagating modes increases with increasing number of viscoelastic layers and higher order modes dissipate significantly less at high frequencies than the lower order modes at low frequencies. Over the frequency range considered, all the circumferential propagating modes are significantly more attenuating than their axial propagating counterparts studied in Part 1 of the paper. Generation of the lowest shear wave mode is suppressed at approximately 0.2 MHz in the coated tubular. However, no such definitive cutoff frequencies are observed for the longitudinal modes regardless of how many viscoelastic layers are considered.