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On the Dispersion and Attenuation of Guided Waves in Tubular Section with Multi-Layered Viscoelastic Coating — Part I: Axial Wave Propagation

Nonlinear Engineering and Control Lab, Mechanical Engineering Department, Texas A&M University, College Station, Texas 77843, U.S.A.

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C. Steve Suh

Nonlinear Engineering and Control Lab, Mechanical Engineering Department, Texas A&M University, College Station, Texas 77843, U.S.A.

E-mail Address: ssuh@tamu.edu

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https://doi.org/10.1142/S1758825117500016Cited by:9 (Source: Crossref)

Abstract

Guided modes admissible in elastic hollow pipes are derived to establish their dispersion and attenuation characteristics in the presence of multi-layered viscoelastic coatings. Longitudinal waves propagating in the axial direction in response to displacement continuity boundary conditions signifying perfect interfacial bonds are evaluated against a baseline uncoated tubing. Viscoelastic bitumen and epoxy are coating materials applied to improve pipeline reliability. The impact of viscoelastic coating layers on wave dispersion and attenuation are investigated by incorporating complex material properties in the characteristic equation. The real and complex roots of the corresponding characteristic equation are determined, allowing the phase velocity and attenuation dispersion to be depicted as functions of the propagation frequency. The effects of varying attenuation parameter and coating thickness are also examined. Viscoelastic protective materials are found to have a substantial impact on the propagation and attenuation of longitudinal waveguide modes.

Keywords:

References

Christensen, R. M. [1981] Theory of Viscoelasticity: An Introduction (Academic, New York). Google Scholar
Barshinger, J. N. and Rose, J. L. [2004] “ Guided wave propagation in an elastic hollow cylinder coated with a viscoelastic material,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 51(11), 1547–1556. Crossref, Web of Science, Google Scholar
Duan, W., Kirby, R., Mudge, P. and Gan, T. H. [2016] “ A one dimensional numerical approach for computing the eigenmodes of elastic waves in buried pipelines,” Journal of Sound and Vibration 384, 177–193. Crossref, Web of Science, Google Scholar
El-Hussein, S., Harrigan, J. J. and Starkey, A. [2015] “ Finite element simulation of guided waves in pipelines for long range monitoring against third party attacks,” Journal of Physics: Conference Series 628(1), 012039. Crossref, Google Scholar
Gong, J., Zecchin, A. C., Lambert, M. F. and Simpson, A. R. [2016] “ Determination of the creep function of viscoelastic pipelines using system resonant frequencies with hydraulic transient analysis,” Journal of Hydraulic Engineering 142(1), 04016023. Crossref, Web of Science, Google Scholar
Jia, H., Mu, J. and Rose, J. L. [2010] “ Guided wave propagation in single and double layer hollow cylinders embedded in infinite media,” The Journal of the Acoustical Society of America 129(2), 691–700. Crossref, Web of Science, Google Scholar
Jones, J. P. [1964] “ Wave propagation in a two-layered medium,” Journal of Applied Mechanics 31, 213–222. Crossref, Google Scholar
Kley, M., Valle, C., Jacobs, L. J., Qu, J. and Jarzynski, J. [1999] “ Development of dispersion curves for two-layered cylinders using laser ultrasonics,” The Journal of the Acoustical Society of America 106(2), 582–588. Crossref, Web of Science, Google Scholar
Knopoff, L. [1964] “ A matrix method for elastic wave problems,” Bulletin of the Seismological Society of America 54(1), 431–438. Crossref, Google Scholar
Kundu, T. [2016] “ Guided waves for plate and pipe inspection,” in Ultrasonic and Electromagnetic NDE for Structure and Material Characterization: Engineering and Biomedical Applications (CRC Press, Florida). Crossref, Google Scholar
Laperre, J. and Thys, W. [1993] “ Experimental and theoretical study of Lamb wave dispersion in aluminum/polymer bilayers,” The Journal of the Acoustical Society of America 94(1), 268–278. Crossref, Web of Science, Google Scholar
Leinov, E., Lowe, M. J. S. and Cawley, P. [2015] “ Investigation of guided wave propagation and attenuation in pipe buried in sand,” Journal of Sound and Vibration 347, 96–114. Crossref, Web of Science, Google Scholar
Liu, Y., Han, Q., Li, C., Liu, X. and Wu, B. [2015] “ Guided wave propagation and mode differentiation in the layered magneto-electro-elastic hollow cylinder,” Composite Structures 132, 558–566. Crossref, Web of Science, Google Scholar
Lowe, M. J. S. [1995] “ Matrix techniques for modeling ultrasonic waves in multilayered media,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 42(4), 525–542. Crossref, Web of Science, Google Scholar
Luo, W. and Rose, J. L. [2007] “ Phased array focusing with guided waves in a viscoelastic coated hollow cylinder,” The Journal of the Acoustical Society of America 121(4), 1945–1955. Crossref, Web of Science, Google Scholar
Mu, J. and Rose, J. L. [2008] “ Guided wave propagation and mode differentiation in hollow cylinders with viscoelastic coatings,” The Journal of the Acoustical Society of America 124(2), 866–874. Crossref, Web of Science, Google Scholar
Nayfeh, A. H. and Nagy, P. B. [1997] “ Excess attenuation of leaky Lamb waves due to viscous fluid loading,” The Journal of the Acoustical Society of America, 101(5), 2649–2658. Crossref, Web of Science, Google Scholar
Pang, M., Zhang, Y. Q. and Chen, W.Q. [2015] “ Transverse wave propagation in viscoelastic single-walled carbon nanotubes with small scale and surface effects,” Journal of Applied Physics 117(2), 024305. Crossref, Web of Science, Google Scholar
Predoi, M. V. and Petre, C. C. [2015] “ Thin wall pipe ultrasonic inspection through paint coating,” Physics Procedia 70, 287–291. Crossref, Google Scholar
Qi, M. X., Zhang, P. G., Ni, J. and Zhou, S. P. [2015] “ Experiment and numerical simulation of ultrasonic guided wave propagation in bent pipe,” Procedia Engineering 130, 1603–1611. Crossref, Google Scholar
Quintanilla, Q. F. H., Fan, Z., Lowe, M. J. S. and Craster, R. V. [2015] “ Guided waves’ dispersion curves in anisotropic viscoelastic single-and multi-layered media,” Proceedings of Royal Society A 471(2183), 20150268. Crossref, Web of Science, Google Scholar
Ray, K., Zlatev, Z. and Mudge, P. [2013] “ On the scattering of longitudinal elastic waves from axisymmetric defects in coated pipes,” Journal of Sound and Vibration 332(20), 5040–5058. Crossref, Web of Science, Google Scholar
Rose, J. L. [2014] Ultrasonic Guided Waves in Solid Media (Cambridge University Press, Cambridge). Crossref, Google Scholar
Schwab, F. [1970] “ Surface wave dispersion computations: Knopoff’s method,” Bulletin of the Seismological Society of America 60(5), 1491–1520. Crossref, Web of Science, Google Scholar
Simonetti, F. [2004] “ Lamb wave propagation in elastic plates coated with viscoelastic materials,” The Journal of the Acoustical Society of America 115(5), 2041–2053. Crossref, Web of Science, Google Scholar
Sonia, D. and Fouad, B., [2010] “ Propagation of guided waves in a hollow circular cylinder application to non destructive testing,” EBJ Web of Conference 6, 15004. Google Scholar
Valle, C., Qu, J. and Jacobs, L. J. [1999] “ Guided circumferential waves in layered cylinders,” International Journal of Engineering Science 37(11), 1369–1387. Crossref, Web of Science, Google Scholar
Zhu, Z. and Wu, J. [1995] “ The propagation of Lamb waves in a plate bordered with a viscous liquid,” The Journal of the Acoustical Society of America 98(2), 1057–1064. Crossref, Web of Science, Google Scholar