Acta Mechanica

, Volume 230, Issue 1, pp 367–380 | Cite as

Complete guided wave modes in piezoelectric cylindrical structures with fan-shaped cross section using the modified double orthogonal polynomial series method

  • B. Zhang
  • J. G. Yu
  • Y. C. WangEmail author
  • L. J. Li
  • X. M. Zhang
Original Paper


The complete guided wave modes are made up of propagative wave modes and evanescent wave modes whose amplitudes exhibit an exponential or damped attenuation with propagation distance. The solutions for evanescent modes are complex and very difficult to be solved. The conventional method usually needs an iterative search procedure to find the complex roots. Accordingly, the modified double orthogonal polynomial series method, an analytical treatment, is proposed to investigate the complex guided waves in piezoelectric cylindrical structures with fan-shaped cross section. By the present method, the real, imaginary and complex solutions are simultaneously obtained without iterative process. Compared with available reference results, the correctness of the proposed method is confirmed. The displacement and electric potential distributions are illustrated, and the piezoelectric effect is detailed. Results reveal that there are some evanescent wave modes, which have much higher velocities than the propagative modes and simultaneously have very low attenuation. The piezoelectric effect can be adjusted by changing the geometric size of the cross section.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors gratefully acknowledge the support by the National Natural Science Foundation of China (No. U1504106) and the Foundation of innovative research team of Henan Polytechnic University (T2017-3) and the Fundamental Research Funds for the Universities of Henan Province (No. NSFRF140301).


  1. 1.
    Zhang, S., Yu, F.: Piezoelectric materials for high temperature sensor. J. Am. Ceram. Soc. 94(10), 3153–3170 (2011)CrossRefGoogle Scholar
  2. 2.
    Grace, J.L.: The utilization of piezoelectric materials and optical fiber sensors for electric field detection. Macromol. Rapid Commun. 35(3), 360–366 (2014)CrossRefGoogle Scholar
  3. 3.
    Qiu, J., Hongli, J.I.: Research on applications of piezoelectric materials in smart structures. Front. Mech. Eng. China 6(1), 99–117 (2011)Google Scholar
  4. 4.
    Nan, C.W., Bichurin, M.I., Dong, S.: Multiferroic magnetoelectric composites: historical perspective, status, and future directions. J. Appl. Phys. 103(3), 031101 (2008)CrossRefGoogle Scholar
  5. 5.
    Yu, J., Wu, B., Chen, G.: Wave characteristics in functionally graded piezoelectric hollow cylinders. Arch. Appl. Mech. 79(9), 807–824 (2009)CrossRefGoogle Scholar
  6. 6.
    Yu, J., Qiujuan, M.: Circumferential wave in functionally graded piezoelectric cylindrical curved plates. Acta Mech. 198(3–4), 171–190 (2008)zbMATHGoogle Scholar
  7. 7.
    Muhammad, I., Bai, H.: Circumferential and spiral waves in piezoelectric cylinders. Adv. Mater. Res. 622, 142–146 (2012)CrossRefGoogle Scholar
  8. 8.
    Cao, L.Y., Cao, X.S.: Circumferential SH waves in piezoelectric layered cylinder for covered layer and substrate in opposite polarization. In: Symposium on Piezoelectricity, Acoustic Waves and Device Applications, pp. 340–344 (2014)Google Scholar
  9. 9.
    Han, X., Liu, G.R.: Elastic waves in a functionally graded piezoelectric cylinder. Smart Mater. Struct. 12(6), 962–971 (2003)CrossRefGoogle Scholar
  10. 10.
    Han, X., Liu, G.R., Ohyoshi, T.: Dispersion and characteristic surfaces of waves in hybrid multilayered piezoelectric circular cylinders. Comput. Mech. 33(5), 334–344 (2004)CrossRefGoogle Scholar
  11. 11.
    Zhao, X., Wang, H.J.: Shear horizontal waves in orthotropic layer/piezoelectric cylinder structures. Adv. Mater. Res. 905, 105–108 (2014)CrossRefGoogle Scholar
  12. 12.
    Zhu, J., Chen, W.Q., Ye, G.R.: Waves in fluid-filled functionally graded piezoelectric hollow cylinders: a restudy based on the reverberation-ray matrix formulation. Wave Motion 50(3), 415–427 (2013)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Vladimir, P., Valeriy, S.: Control of elastic wave propagation in piezoceramic cylinders of sector cross section. Solid Mech. Appl. 30, 215–222 (2011)MathSciNetGoogle Scholar
  14. 14.
    Zhou, Y.Y., Chen, W.Q., Lu, C.F.: Elastic waves in piezoelectric cylinders with sectorial cross-section. In: Symposium on Piezoelectricity, Acoustic Waves and Device Applications, pp. 319–324 (2010)Google Scholar
  15. 15.
    Puzyrev, V.: Elastic waves in piezoceramic cylinders of sector cross-section. Int. J. Solids Struct. 47, 2115–2122 (2010)CrossRefGoogle Scholar
  16. 16.
    Awrejcewicz, J., Storozhev, V., Puzyrev, V.: Controlling the dynamic behavior of piezoceramic cylinders by cross-section geometry. Acta Mech. 223(6), 1119–1136 (2012)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Graczykowski, B., Alzina, F., Gomisbresco, J.: Finite element analysis of true and pseudo surface acoustic waves in one-dimensional phononic crystals. J. Appl. Phys. 119(2), 025308 (2016)CrossRefGoogle Scholar
  18. 18.
    Roshchupkin, D., Ortega, L., Plotitcyna, O.: X-ray imaging of the surface acoustic wave propagation in \(\text{ La }_{3}\text{ Ga }_{5}\text{ SiO }_{14}\) crystal. Appl. Phys. Lett. 103(15), 154101 (2013)CrossRefGoogle Scholar
  19. 19.
    Glushkov, E., Glushkova, N., Zhang, C.: Surface and pseudo-surface acoustic waves piezoelectrically excited in diamond-based structures. J. Appl. Phys. 112(112), 064911 (2012)CrossRefGoogle Scholar
  20. 20.
    Zhang, B., Yu, J.G., Zhang, X.M.: Guided wave propagation in cylindrical structures with sector cross-sections. Arch. Appl. Mech. 2, 1–12 (2017)Google Scholar
  21. 21.
    Lefebvre, J.E., Yu, J.G., Ratolojanahary, F.E.: Mapped orthogonal functions method applied to acoustic waves-based devices. AIP Adv. 6(6), 065307 (2016)CrossRefGoogle Scholar
  22. 22.
    Liu, Y., Han, Q., Huang, H.: Computation of dispersion relations of functionally graded rectangular bars. Compos. Struct. 133(98), 31–38 (2015)CrossRefGoogle Scholar
  23. 23.
    Zhang, X., Xu, X., Wang, Y.: Wave propagation in piezoelectric rods with rectangular cross sections. J. Theor. Appl. Mech. 53(3), 673–682 (2014)zbMATHGoogle Scholar
  24. 24.
    Guo, Y.Q., Chen, W.Q., Zhang, Y.L.: Guided wave propagation in multilayered piezoelectric structures. Sci. China 52(7), 1094–1104 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • B. Zhang
    • 1
  • J. G. Yu
    • 1
  • Y. C. Wang
    • 2
    Email author
  • L. J. Li
    • 3
  • X. M. Zhang
    • 1
  1. 1.School of Mechanical and Power EngineeringHenan Polytechnic UniversityJiaozuoPeople’s Republic of China
  2. 2.School of Materials Science and EngineeringHenan Polytechnic UniversityJiaozuoPeople’s Republic of China
  3. 3.Department of Basic TeachingHuanghe Jiaotong UniversityJiaozuoPeople’s Republic of China

Personalised recommendations