Scattering of Anti-Plane Shear Waves by a Single Crack in an Unbounded Transversely Isotropic Electro-Magneto-Elastic Medium

DU Jian-ke; SHEN Ya-peng; GAO Bo

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(12): 1230-1238

DU Jian-ke, SHEN Ya-peng, GAO Bo. Scattering of Anti-Plane Shear Waves by a Single Crack in an Unbounded Transversely Isotropic Electro-Magneto-Elastic Medium[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1230-1238.

Citation:

PDF( 2306 KB)

Scattering of Anti-Plane Shear Waves by a Single Crack in an Unbounded Transversely Isotropic Electro-Magneto-Elastic Medium

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

Received Date: 2003-12-20
Rev Recd Date: 2004-06-29
Publish Date: 2004-12-15

Abstract

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 differ ential 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 bo undary conditions.The closed for m 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.
- electro-magneto-elasticity,
- SH wave,
- stress intensity factor,
- integral equation

FullText(HTML)

References(13)

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. doi: 10.1016/0022-5096(91)90006-A
[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. doi: 10.1007/BF02878719
[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. doi: 10.1016/0020-7683(95)00179-4
[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.
[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. doi: 10.1016/0020-7683(82)90099-3
[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. doi: 10.1007/BF01182354
[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. doi: 10.1007/BF01170302
[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. doi: 10.1016/S0167-6636(00)00043-0
[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.
[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. doi: 10.1016/0020-7683(95)00062-F
[11]	Huang J H, Kuo W S.The analysis of piezoelectric/piezomagnetic composite materials containing an ellipsoidal inclusion[J].Journal of Applied Physics,1997,81(3):1378—1386. doi: 10.1063/1.363874
[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. doi: 10.1115/1.1380385
[13]	WANG X,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. doi: 10.1016/S0020-7225(02)00006-X