Applied Mathematics and Mechanics

, Volume 28, Issue 9, pp 1227–1234 | Cite as

Propagation of slip pulse along frictionless contact interface with local separation between two piezoelectric solids

  • Bai Yu-zhu  (白玉柱)
  • Wang Yue-sheng  (汪越胜)Email author
  • Yu Gui-lan  (于桂兰)


The Stroh formalism of piezoelectric materials, Fourier analysis and singular integral equation technique were used to investigate the existence of a pulse at the frictionless interface in presence of local separation between two contact piezoelectric solids. The two solids were combined together by uniaxial tractions and laid in the electric field. The problem was cast into a set of Cauchy singular integral equations, from which the closed-form solutions were derived. The numerical discussion on the existence of such a slip pulse was presented. The results show that such a slip pulse, which has square root singularities at both ends of the local separation zone, can propagate in most material combinations. And the existence of such a slip pulse will not be affected by the applied mechanical and electric fields in some special material combinations.

Key words

interface piezoelectric material singular integral equation slip pulse Stroh formalism 

Chinese Library Classification


2000 Mathematics Subject Classification

45E05 74F15 74M15 


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  1. [1]
    Tiersten H F. Linear piezoelectric plate vibrations[M]. New York: Plenum, 1969.Google Scholar
  2. [2]
    Balakirev M K, Gilinskyi Y A. Waves in piezocrystals[M]. Akad Nauk USSR: Novosibirsk, 1982 (in Russian).Google Scholar
  3. [3]
    Auld B A. Acoustic fields and waves in solid[M]. New York: John Wiley, 1973.Google Scholar
  4. [4]
    Nayfeh A H. Wave propagation in layered anisotropic media[M]. Amsterdam: Elsevier, 1995.Google Scholar
  5. [5]
    Kurosawa M, Ueha S. Efficiency of ultrasonic motor using traveling wave[J]. Journal of Acoustic Society of Japan, 1988, 44:40–46 (in Japanese).Google Scholar
  6. [6]
    Comninou M, Dundurs J, Barber J R. Elastic interface waves involving separation[J]. Journal of Applied Mechanics, 1977, 44:222–226.Google Scholar
  7. [7]
    Comninou M, Dundurs J. Elastic interface waves and sliding between two solids[J]. Journal of Applied Mechanics, 1978, 45:325–330.zbMATHGoogle Scholar
  8. [8]
    Wang Y S, Yu G L, Zhang Z M, Feng Y D. Review on elastic wave propagation under complex interface (interface layer) conditions[J]. Advance in Mechanics, 2000, 30(3):378–390 (in Chinese).Google Scholar
  9. [9]
    Wang Y S, Dai H H, Yu G L. Non-linear interaction of an elastic pulse with a friction contact interface between two anisotropic dissimilar media[J]. Journal of Vibration and Acoustics, 2004, 126(1):108–117.CrossRefGoogle Scholar
  10. [10]
    Yu G L, Wang Y S. Slip pulse along an interface between two anisotropic elastic half-spaces in sliding contact with separation[J]. Archive of Applied Mechanics, 2006, 75(4/5):210–219.zbMATHCrossRefGoogle Scholar
  11. [11]
    Li N, Wang Y S, Yu G L. Analysis of dynamic instability of interfacial slip waves based on the surface impedance tensor[J]. Applied Mathematics and Mechanics, 2004, 25(9):1022–1030.zbMATHCrossRefGoogle Scholar
  12. [12]
    Alshits V I, Barnett D M, Darinskii A N, Lothe J. On the existence problem for localized acoustic waves on the interface between two piezocrystals[J]. Wave Motion, 1994, 20:233–244.zbMATHCrossRefGoogle Scholar
  13. [13]
    Darinskii A N, Weihnacht M. Interface waves on the sliding contact between identical piezoelectric crystals of general anisotropy[J]. Wave Motion, 2005, 43:67–77.CrossRefGoogle Scholar
  14. [14]
    Ting T C T. Anisotropic elasticity, theory and applications[M]. New York: Oxford University Press, 1996.Google Scholar
  15. [15]
    Muskhelishvili N L. Singular integral equations[M]. Noordhoff, The Netherland: Groningen, 1958.Google Scholar

Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Bai Yu-zhu  (白玉柱)
    • 1
  • Wang Yue-sheng  (汪越胜)
    • 1
    Email author
  • Yu Gui-lan  (于桂兰)
    • 1
  1. 1.School of Civil Engineering and ArchitectureBeijing Jiaotong UniversityBeijingP. R. China

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