, Volume 54, Issue 1–2, pp 169–182 | Cite as

Wave isogeometric analysis method for calculating dispersive properties of guided waves in rotating damped cylinders

  • Chunlei Li
  • Qiang HanEmail author
  • Yijie Liu
  • Zhan Wang


The reliable guided wave inspection techniques depend on the accurate understanding of dispersive properties. The classic finite element method has been proven to be very practical for modeling wave propagation in arbitrary waveguides. However, when it comes to modeling on complex geometries, it still has a major drawback: the geometric discrete errors and the high consumption of resources to improve accuracy. Recently, Isogeometric analysis has been found advantageous over the classic finite element method on geometry representation and mesh generation. Here, a wave isogeometric analysis (WIGA) method is proposed for the computation of guided wave characteristics in rotating damped cylinders, based on the Floquet’s principle. According to the linear incremental theory and the principle of virtual power, elastodynamic wave equation is established, with regard to the WIGA. To ensure its effectiveness, the convergence and accuracy of the proposed method are considered compared with that of the wave finite element method. The size of unit cell and the solvable frequency range are discussed in detail. Furthermore, dispersive behaviors are computed considering the effects of damping and rotation. The results demonstrate that flexural wave modes are very sensitive to the rotation effect. Particularly, in phase velocity spectra the characteristic frequency at the amplitude peak equals to the rotational angular speed, where wave propagating and attenuating both vanish.


Wave isogeometric analysis Elastic waves Dispersive properties Rotation Damping 



The authors wish to acknowledge the support from the Natural Science Foundation of China (11472108 and 11772130).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

11012_2018_921_MOESM1_ESM.rar (1.1 mb)
Supplementary material 1 (rar 1106 KB)


  1. 1.
    Rose JL (2004) Ultrasonic waves in solid media. Cambridge University Press, CambridgeGoogle Scholar
  2. 2.
    Benmeddour F, Treyssde F, Laguerre L (2011) Numerical modeling of guided wave interaction with non-axisymmetric cracks in elastic cylinders. Int J Solid Struct 48(5):764–774CrossRefzbMATHGoogle Scholar
  3. 3.
    Mace BR, Duhamel D, Brennan MJ, Hinke L (2005) Finite element prediction ofwave motion in structural waveguides. J Acoust Soc Am 117(5):2835–2843ADSCrossRefGoogle Scholar
  4. 4.
    Brillouin L (1953) Wave propagation in periodic structures: Electric filters and crystal lattices. McGraw-Hill Book Company, New YorkzbMATHGoogle Scholar
  5. 5.
    Mead DM (1996) Wave propagation in continuous periodic structures: research contributions from southampton, 1964–1995. J Sound Vib 190(3):495–524ADSCrossRefGoogle Scholar
  6. 6.
    Manconi E, Mace BR (2009) Wave characterization of cylindrical and curved panels using a finite element method. J Acoust Soc Am 125(1):154–163ADSCrossRefGoogle Scholar
  7. 7.
    Waki Y, Mace BR, Brennan MJ (2009) Free and forced vibrations of a tyre using a wave/finite element approach. J Sound Vib 323(3):737–756ADSCrossRefGoogle Scholar
  8. 8.
    Mencik JM (2014) New advances in the forced response computation of periodic structures using the wave finite element (wfe) method. Comput Mech 54(3):789–801MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kharrat M, Ichchou MN, Bareille O, Zhou WJ (2014) Pipeline inspection using a torsional guided-waves inspection system. part 1: defect identification. Int J Appl Mech 6(04):1450034CrossRefGoogle Scholar
  10. 10.
    Huang TL, Ichchou MN, Bareille OA, Collet M, Ouisse M (2013) Traveling wave control in thin-walled structures through shunted piezoelectric patches. Mech Syst Signal Pr 39(1):59–79CrossRefzbMATHGoogle Scholar
  11. 11.
    Zhou WJ, Ichchou MN (2010) Wave propagation in mechanical waveguide with curved members using wave finite element solution. Comput Method Appl M 199(33):2099–2109MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Li CL, Han Q, Liu YJ, Liu XC, Wu B (2015) Investigation of wave propagation in double cylindrical rods considering the effect of prestress. J Sound Vib 353:164–180ADSCrossRefGoogle Scholar
  13. 13.
    Souf MAB, Bareille O, Ichchou MN, Bouchoucha F, Haddar M (2013) Waves and energy in random elastic guided media through the stochastic wave finite element method. Phys Lett A 377(37):2255–2264ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Zienkiewicz OC, Taylor RL, Taylor RL (1997) The finite element method, vol 3. McGraw-hill, LondonzbMATHGoogle Scholar
  15. 15.
    Wang YY, Lam KY, Liu GR (2001) A strip element method for the transient analysis of symmetric laminated plates. Int J Solid Struct 38(2):241–259CrossRefzbMATHGoogle Scholar
  16. 16.
    Xi ZC, Liu GR, Lam KY, Shang HM (2000) A strip-element method for analyzing wave scattering by a crack in a fluid-filled composite cylindrical shell. Compos Sci Technol 60(10):1985–1996CrossRefGoogle Scholar
  17. 17.
    Liu YJ, Han Q, Li CL, Huang HW (2014) Numerical investigation of dispersion relations for helical waveguides using the scaled boundary finite element method. J Sound Vib 333(7):1991–2002ADSCrossRefGoogle Scholar
  18. 18.
    Gravenkamp H, Song CM, Prager J (2012) A numerical approach for the computation of dispersion relations for plate structures using the scaled boundary finite element method. J Sound Vib 331(11):2543–2557ADSCrossRefGoogle Scholar
  19. 19.
    Treyssde F (2016) Spectral element computation of high-frequency leaky modes in three-dimensional solid waveguides. J Comput Phys 314:341–354ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: cad, finite elements, nurbs, exact geometry and mesh refinement. Comput Method Appl M 194(39):4135–4195MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Xu G, Mourrain B, Duvigneau R, Galligo A (2013) Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications. Comput Aided Des 45(2):395–404MathSciNetCrossRefGoogle Scholar
  22. 22.
    Yu P, Anitescu C, Tomar S, Bordas SPA, Kerfriden P (2018) Adaptive Isogeometric analysis for plate vibrations: an efficient approach of local refinement based on hierarchical a posteriori error estimation. Comput Method Appl M 342:251–286MathSciNetCrossRefGoogle Scholar
  23. 23.
    Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the jarvik 2000 left ventricular assist device. Comput Method Appl M 198(45):3534–3550MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Shojaee S, Valizadeh N, Izadpanah E, Bui T, Vu TV (2012) Free vibration and buckling analysis of laminated composite plates using the nurbs-based isogeometric finite element method. Compos Struct 94(5):1677–1693CrossRefGoogle Scholar
  25. 25.
    De-Lorenzis L, Temizer I, Wriggers P, Zavarise G (2011) A large deformation frictional contact formulation using nurbs-based isogeometric analysis. Int J Numer Meth Eng 87(13):1278–1300MathSciNetzbMATHGoogle Scholar
  26. 26.
    Wall WA, Frenzel MA, Cyron C (2008) Isogeometric structural shape optimization. Comput Method Appl M 197(33):2976–2988MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Khajah T, Antoine X, Bordas S (2016). Isogeometric finite element analysis of time-harmonic exterior acoustic scattering problems. ArXiv preprint arXiv:1610.01694
  28. 28.
    Videla J, Anitescu C, Khajah T, Bordas S, Atroshchenko E (2018) h-and p-adaptivity driven by recovery and residual-based error estimators for PHT-splines applied to time-harmonic acoustics.
  29. 29.
    Simpson RN, Bordas SP, Trevelyan J, Rabczuk T (2012) A two-dimensional isogeometric boundary element method for elastostatic analysis. Comput Method Appl M 209:87–100MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Simpson RN, Scott MA, Taus M, Thomas DC, Lian H (2014) Acoustic isogeometric boundary element analysis. Comput Method Appl M 269:265–290MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Peake MJ, Trevelyan J, Coates G (2015) Extended isogeometric boundary element method (XIBEM) for three-dimensional medium-wave acoustic scattering problems. Comput Method Appl M 284:762–780MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Gravenkamp H, Natarajan S, Dornisch W (2017) On the use of NURBS-based discretizations in the scaled boundary finite element method for wave propagation problems. Comput Method Appl M 315:867–880MathSciNetCrossRefGoogle Scholar
  33. 33.
    Katsikadelis JT (2002) Boundary elements: theory and applications. Elsevier, AmsterdamGoogle Scholar
  34. 34.
    Bathe KJ (1996) Finite element procedures. Prentice-hall, Englewood CliffszbMATHGoogle Scholar
  35. 35.
    Waki Y, Mace BR, Brennan MJ (2009) Numerical issues concerning the wave and finite element method for free and forced vibrations of waveguides. J Sound Vib 327:92–108ADSCrossRefGoogle Scholar
  36. 36.
    Brillouin L (1946) Wave propagation in periodic structures, 2nd edn. Dover, Downers GrovezbMATHGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Civil Engineering and TransportationSouth China University of TechnologyGuangzhouPeople’s Republic of China
  2. 2.State Key Laboratory of Subtropical Building ScienceSouth China University of TechnologyGuangzhouChina
  3. 3.School of Civil EngineeringGuangzhou UniversityGuangzhouChina

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