Skip to main content
SpringerLink
Log in

Scattering of anti-plane shear waves by a single crack in an unbounded trasversely isotropic electro-magneto-elastic medium

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

A theoretical treatment of the scattering of anti-plane shear (SH) waves is provided by a single crack in an unbounded transversely isotropic electro-magneto-elastic medium. Based on the differential equations of equilibrium, electric displacement and magnetic induction intensity differential equations, the governing equations for SH waves were obtained. By means of a linear transform, the governing equations were reduced to one Helmholtz and two Laplace equations. The Cauchy singular integral equations were gained by making use of Fourier transform and adopting electro-magneto impermeable boundary conditions. The closed form expression for the resulting stress intensity factor at the crack was achieved by solving the appropriate singular integral equations using Chebyshev polynomial. Typical examples are provided to show the loading frequency upon the local stress fields around the crack tips. The study reveals the importance of the electro-magneto-mechanical coupling terms upon the resulting dynamic stress intensity factor.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Yang Y, Norris A N. Shear wave scattering from a debonded fiber[J].Journal of Mechanics and Physics of Solids, 1991,39(2):273–294.

    Article  Google Scholar 

  2. Wang X M, Ying C F. Scattering of guided SH-wave by a partly debonded circular cylinder in a traction free plate[J].Science in China, Series A, 2001,44(3):378–388.

    Article  Google Scholar 

  3. Wang Y S, Wang D. Scattering of elastic waves by a rigid debonded from its surrounding matrix — I: SH case[J].International Journal of Solids and Structures, 1996,33(19):2789–2815.

    Article  MATH  Google Scholar 

  4. Zhou Z G, Shen Y P. Scattering of harmonic elastic waves by a plane interface crack with linear adhesive tips in a layered half space[J].Acta Mechanica Solida Sinica, 1994,7(2):105–113.

    Article  Google Scholar 

  5. Ryan R L, Mall S. Scattering of antiplane shear waves by a submerged crack[J].International Journal of Solids and Structures, 1982,18(12):1145–1152.

    Article  MATH  Google Scholar 

  6. Zhou Z G, Li H C, Wang B. Investigation of the scattering of anti-plane shear waves by two collinear cracks in a piezoelectric material using a new method[J].Acta Mechanica, 2001,147(1): 87–97.

    Article  MATH  Google Scholar 

  7. Narita F, Shindo Y. Scattering of antiplane shear waves by a finite crack in piezoelectric laminates [J].Acta Mechanica, 1999,134(1):27–43.

    Article  MATH  MathSciNet  Google Scholar 

  8. Wang X D, Meguid S A. Modeling and analysis of the dynamic behavior of piezoelectric materials containing interacting cracks[J].Mechanics of Materials, 2000,32(7):723–737.

    Article  Google Scholar 

  9. Wang X D. On the dynamic behavior of interaction interfacial cracks in piezoelectric media[J].International Journal of Solids and Structures, 2001,38(8):851–831.

    Article  Google Scholar 

  10. Wang X M, Shen Y P. The conservation laws and path-independent integrals for linear electro-magneto-elastic media with an application[J].International Journal of Solids and Structures, 1996,33 (8):865–878.

    Article  MATH  Google Scholar 

  11. Huang J H, Kuo K S. The analysis of piezoelectric/piezomagnetic composite materials containing an ellipsoidal inclusion[J].Journal of Applied Physics, 1997,81(3):1378–1386.

    Article  Google Scholar 

  12. Pan E. Exact solution for simply supported and multilayered magneto-electro-elastic plates[J].ASME Journal of Applied Mechanics, 2001,68(6):608–618.

    Article  MATH  Google Scholar 

  13. WANG Xu, Shen Y P. The general solution of three-dimensional problem in magneto-electro-elastic media[J].International Journal of Engineering Science, 2002,40(10):1069–1080.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Mechanical Structural Strength and Vibration, Xi'an Jiaotong University, 710049, Xi'an, PR China

    Du Jian-ke Associate Professor, Doctor & Shen Ya-peng

  2. Fourth Academy of CASC, 710025, Xi'an, PR China

    Du Jian-ke Associate Professor, Doctor & Gao Bo

Authors
  1. Du Jian-ke Associate Professor, Doctor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shen Ya-peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gao Bo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shen Ya-peng.

Additional information

Contributed by SHEN Ya-peng

Foundation item: the National Natural Science Foundation of China (10132010, 50135030)

Biographies: DU Jian-ke (1970∼)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jian-ke, D., Ya-peng, S. & Bo, G. Scattering of anti-plane shear waves by a single crack in an unbounded trasversely isotropic electro-magneto-elastic medium. Appl Math Mech 25, 1344–1353 (2004). https://doi.org/10.1007/BF02438291

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02438291

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation