Scattering of Anti-Plane Shear Waves by a Single Crack in an Unbounded Transversely Isotropic Electro-Magneto-Elastic Medium
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摘要: 研究横观各向同性电磁弹性介质中裂纹和反平面剪切波之间的相互作用.根据电磁弹性介质的平衡运动微分方程、电位移和磁感应强度微分方程,得到SH波传播的控制场方程.引入线性变换,将控制场方程简化为Helmholtz方程和两个Laplace方程A·D2通过Fourier变换,并采用非电磁渗透型裂面边界条件,得到了柯西奇异积分方程组.利用Chebyshev多项式求解积分方程,得到应力场、电场和磁场以及动应力强度因子的表达,并给出了数值算例.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.
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Key words:
- electro-magneto-elasticity /
- SH wave /
- stress intensity factor /
- integral equation
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[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
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