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, Vol. 25 ›› Issue (12): 1344-1353.

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

杜建科^1,2, 沈亚鹏¹, 高波²

1. State Key Laboratory of Mechanical Structural Strength and Vibration, Xi'an Jiaotong University, Xi'an, 710049, P. R. China;
2. Fourth Academy of CASC, Xi'an 710025, P. R. China

收稿日期:2003-12-20 修回日期:2004-06-29 出版日期:2004-12-18 发布日期:2004-12-18
通讯作者: SHEN Ya-peng Corresponding author,(Tel:+ 86-29-82668751:Fax:+86-29-83237910:E-mail:ypshen@xjtu.edu.cn) E-mail:ypshen@xjtu.edu.cn
基金资助:
the National Natural Science Foundation of China (10132010, 50135030)

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

DU Jian-ke^1,2, Shen Ya-peng¹, Gao Bo²

1. State Key Laboratory of Mechanical Structural Strength and Vibration, Xi'an Jiaotong University, Xi'an, 710049, P. R. China;
2. Fourth Academy of CASC, Xi'an 710025, P. R. China

Received:2003-12-20 Revised:2004-06-29 Online:2004-12-18 Published:2004-12-18
Supported by:
the National Natural Science Foundation of China (10132010, 50135030)

摘要/Abstract

摘要： 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.

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.

中图分类号:

O343
70K25

杜建科;沈亚鹏;高波. SCATTERING OF ANTI-PLANE SHEAR WAVES BY A SINGLE CRACK IN AN UNBOUNDED TRANSVERSELY ISOTROPIC ELECTRO-MAGNETO-ELASTIC MEDIUM[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(12): 1344-1353.

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 (English Edition), 2004, 25(12): 1344-1353.

参考文献

[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]	任九生程昌钧. 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]	李卫国;成天宝;张如炳;方岱宁. 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]	傅向荣;袁明武;岑松;田歌. 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]	赵莉;陈伟球;吕朝锋. 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]	吕和祥李俊永. Vibration and stability of hybrid plate based on elasticity theory[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(4): 413-423.
[8]	曹志远;唐寿高;程国华. 复杂形状及开孔功能梯度板的三维分析[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(1): 13-18 .
[9]	R.库玛;鲁班德. 磁_微极广义热弹性介质中轴对称变形的弹性动力学[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(1): 39-48 .
[10]	A.M.任库尔;K.A.伊莉莎白;D.S.玛沙特. 功能梯度空心及实心圆柱体旋转时的弹性及粘弹性解[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(12): 1601-1616 .
[11]	R.库玛;T.坎赛. 横观各向同性广义热弹性扩散Rayleigh波在自由表面上的传播[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(11): 1451-1462 .
[12]	M.K.戈西;M.卡诺瑞阿. 热冲击载荷作用下的含球形空腔的广义热弹性功能梯度球形各向同性体[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(10): 1263-1278 .
[13]	任九生. 周期载荷下超弹性圆柱壳的动力响应[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(10): 1319-1327 .
[14]	杨博;丁皓江;陈伟球. 功能剃度板柱面弯曲的弹性力学解[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(8): 999-1004 .
[15]	刘又文;李博;方棋洪. 各向异性双材料中运动螺型位错与界面刚性线的干涉[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(5): 625-638 .

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

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

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价