SCATTERING OF ANTI-PLANE SHEAR WAVES BY A SINGLE CRACK IN AN UNBOUNDED TRANSVERSELY ISOTROPIC ELECTRO-MAGNETO-ELASTIC MEDIUM

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 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.

2010 MSC Number:

O343
70K25

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. Applied Mathematics and Mechanics (English Edition), 2004, 25(12): 1344-1353.

TrendMD

References

[1]　Taylor E H. Flow characteristics at rectangular open channel junctions [J]. Trans ASCE, 1944, 109:893-912.
[2]　Ramamurthy A S, Carballada L B, Tran D M. Combining open channel flow at right angled junctions.
[J]. J Hydraulic Engineering, 1988, 114 (12):1449-1460.
[3]　NI Jin-ren, WANG Guang-qian, ZHANG Guo-sheng. Hydraulic calculate in confluent channel [J]. J Hydraulics, 1992, 7 (7):51-56. (in Chinese).
[4]　Hsu C C, Wu F S, Lee W J. Flow at 90°equal-width open-channel junction[J]. J Hydraulic Engi2neering, 1998, 124 (2):186-191.
[5]　Hsu C C, Lee W J, Chang C H. Subcritical open-channel junction flow[J]. J Hydraulic Engineer2ing, 1998, 124 (8):847-855.
[6]　Lakshmana N S, Sridharan L. Discussion of dividing flow in an open channel [J]. J Hydraulic Di2vision ASCE, 1966, 94 (HY6):237-239.
[7]　Ramamurthy A S, Satish M G. Division of flow in short open channel branches [J]. J HydraulicEngineering, 1988, 114 (4):428-438.
[8]　Ramamurthy A S. Dividing flow in open channels [J]. J Hydraulic Engineering, 1990, 116 (3):449-455.
[9]　CHEN Li, MING Zong-fu. Channel Hydrodynamics [M]. Wuhan:Wuhan University Press, 2001, 106-107. (in Chinese).
[10]　J I Xue-wu. The 1998 Yangtze River flood and hydrology technology progress [J]. Yangtze River, 1999, 30 (2):1-5. (in Chinese).
[11]　LI An-tian. The 1998 Yangtze River flood and its prevention [J]. Yangtze River, 1999, 30 (1):1-7. (in Chinese).
[12]　DUAN Wen-zhong, ZHENG Ya-hui. The waterlevel risen for the Yangtze River between Cheng2lingji and Luoshan station and its causing analysis [J]. J Hydraulics, 2001, 2 (2):29-34. (inChinese).
[13]　YU Chang-zhao. Supercritical Flow in Open Channels-Theory and Application in Hydraulics Engi2neering[M]. Beijing:Tsinghua University Press, 1999, 21-22. (in Chinese).
[14]　HUANG Si-ping, WU Ru-fa. Analysis of effect of reservoir on Yangtze flood in 1998[J]. YangtzeRiver, 1999, 30 (2):24-26. (in Chinese).

[1]	REN Jiu-Sheng;CHENG Chang-Jun. Non-uniqueness and stability of two-family fiber-reinforced incompressible hyper-elastic sheet under equibiaxial loading [J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(12): 1513-1520.
[2]	Wei-guo LI;Tian-bao CHENG;Ru-bing ZHANG;Dai-ning FANG. Properties and appropriate conditions of stress reduction factor and thermal shock resistance parameters for ceramics [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(11): 1351-1360.
[3]	M. NAWAZ;T. HAYAT;A.ALSAEDI. Dufour and Soret effects on MHD flow of viscous fluid between radially stretching sheets in porous medium [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(11): 1403-1418.
[4]	Xiang-rong FU;Ming-wu YUAN;Song CEN;Ge TIAN . Characteristic equation solution strategy for deriving fundamental analytical solutions of 3D isotropic elasticity [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(10): 1253-1264.
[5]	Li ZHAO;Wei-qiu CHEN;Chao-feng L�. Two-dimensional complete rational analysis of functionally graded beams within symplectic framework [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(10): 1225-1238.
[6]	A. M. ABD-ALLA;G. A. YAHYA. Thermal stresses in infinite circular cylinder subjected to rotation [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(8): 1059-1078.
[7]	He-Xiang LV;Jun-Yong LI. Vibration and stability of hybrid plate based on elasticity theory [J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(4): 413-423.
[8]	Zhi-yuan CAO;Shougao TANG;Guohua CHENG. 3D analysis of functionally graded material plates with complex shapes and various holes [J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(1): 13-18 .
[9]	Rajneesh Kumar;Rupender. Elastodynamics of axi-symmetric deformation in magneto-micropolar generalized thermoelastic medium [J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(1): 39-48 .
[10]	A. M. Zenkour;K. A. Elsibai and D. S. Mashat. Elastic and viscoelastic solutions to rotating functionally graded hollow and solid cylinders [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(12): 1601-1616 .
[11]	Rajneesh Kumar;Tarun Kansa. Propagation of Rayleigh waves on free surface of transversely isotropic generalized thermoelastic diffusion [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(11): 1451-1462 .
[12]	M. K. Ghosh;M. Kanoria. Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shock [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(10): 1263-1278 .
[13]	REN Jiu-sheng. Dynamical response of hyper-elastic cylindrical shells under periodic load [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(10): 1319-1327 .
[14]	YANG Bo;DING Hao-jiang;CHEN Wei-qiu. Elasticity solutions for functionally graded plates in cylindrical bending [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(8): 999-1004 .
[15]	LIU You-wen;LI Bo;FANG Qi-hong. A moving screw dislocation near interfacial rigid lines in two dissimilar anisotropic media [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(5): 625-638 .