Dynamic stress concentration of a circular cavity near the interface of orthotropic bimaterials under SH wave incidence

PDF(3313 KB)

Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (1) : 301-307.

LAN Guoguan 1, ZHANG Cunfeng1, XU Huanan1, ZHANG Jianwei2

Author information +

History +

Abstract

Based on the complex function method and Green's function, the scattering of SH wave in orthotropic bimaterials with a circular cavity iwas discussed, and the dynamic response around the cavity iwas analyzed. Firstly, the two-dimensional analytical model of the problem iwas established, and the whole space iwas divided into two parts: the homogeneous isotropic upper half space and the orthotropic lower half space with a cylindrical cavity. Using Green's function method, the Green’s function expression of each point at the interface of two half spaces iwas derived, and the complex variable iwas introduced to construct the wave field expression for solving the displacement and stress in the region under the incidence of SH wave. Considering the continuity condition of the interface, the undetermined anti-plane force iwas loaded on the horizontal interface of two half spaces, and then the Fredholm definite solution integral equations awere derived and solved by the direct discretization method of weak singular integral equations. Finally, through the calculation and analysis of examplesthrough a series of calculating analysis, it iwas found that the orthotropic parameters of the medium, the number of incident waves, the angle and the buried depth of the cavity have significant effects on the dynamic stress concentration factor (DSCF) around the circular cavity in the lower half space.
Key words: SH-waves; Green’s function; anisotropic bimaterials interface; circular cavity; DSCF

Key words

SH-waves / Green’s function / anisotropic bimaterials interface / circular cavity / DSCF

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

LAN Guoguan 1, ZHANG Cunfeng1, XU Huanan1, ZHANG Jianwei2. Dynamic stress concentration of a circular cavity near the interface of orthotropic bimaterials under SH wave incidence[J]. Journal of Vibration and Shock, 2023, 42(1): 301-307

References

[1] 刘殿魁, 刘宏伟. 孔边裂纹对SH波散射及动应力强度因子[J]. 力学学报, 1999, 31(3): 292-299.
LIU Diankui, LIU Hongwei. Scattering of SH-wave by cracks originating at a circular hole edge and dynamics tress intensity factor[J]. Acta Mechanica Sinica, 1999, 31(3): 292-299.
[2] 杨在林, 许华南, 黑宝平. 半空间椭圆夹杂与裂纹对SH波的散射[J].振动与冲击, 2013, 32(11): 56-61, 79.
YANG Zailin, XU Huanan, HEI Baoping. Interaction of elliptical inclusion and crack under incident SH-wave in a half-space[J]. Journal of Vibration and Shock, 2013, 32(11): 56-61, 79.
[3] 杨在林, 许华南, 黑宝平. SH波上方垂直入射时界面附近椭圆夹杂与裂纹的动态响应[J]. 岩土力学, 2013.6, 34(8): 2378-2384.
YANG Zailin, XU Huanan, HEI Baoping. Dynamic response of elliptical inclusion and crack near interface under vertically incident SH-wave from above[J]. Rock and Soil Mechanics, 2013.6, 34(8): 2378-2384.
[4] 齐辉, 丁晓浩, 赵元博. 双相介质弹性半空间垂直界面附近椭圆形夹杂对SH波的散射[J]. 振动与冲击, 2015, 34(24): 76-81.
QI Hui, DING Xiaohao, ZHAO Yuanbo. Scattering of SH-wave by an elliptic inclusion near vertical interface in a bi-material half-space [J]. Journal of Vibration and Shock, 2015, 34(24): 76-81.
[5] 杨杰, 齐辉. 半空间中双相介质界面一侧多个圆形弹性孔洞对SH波的散射[J]. 地震工程与工程振动, 2019, 39(6): 128-137.
YANG Jie, QI Hui. Scattering of SH waves by multiple circular elastic holes at the side of bi-material interface in half space [J]. Earthquake Engineering and Engineering Dynamics, 2019, 39(6): 128-137.
[6] Yang Z L, Hei B P, Wang Y. Scattering by a circular cavity in a radially inhomogeneous medium with wave velocity variation [J]. Applied Mathematics and Mechanics (English Edition). 2015. 36 (5): 599-608.
[7] Lee V W, Liu W Y. Two-dimensional scattering and diffraction of P- and SV-waves around a semi-circular canyon in an elastic half-space: an analytic solution via a stress-free wave function [J]. Soil Dynamics and Earthquake Engineering, 2014, 63: 110-119.
[8] 齐辉, 高春, 周亚东, 潘向南, 蔡立明.下部脱胶界面圆夹杂的弹性动力学反平面分析[J].中南大学学报(自然科学版), 2016,47(3): 959-966.
QI Hui, GAO Chun, ZHOU Yadong, PAN Xiangnan, CAI Liming. Anti-plane analysis for steady state elastodynamics of interfacial debonding-bottomed circular inclusions[J]. Journal of Central South University (Science and Technology), 2016, 47(3): 959-966.
[9] Xu H. N., Yang Z. L., Wang S. S. Dynamics Response of Complex Defects near Bimaterials Interface by Incident Out-plane Waves[J]. Acta Mechanica, 2016.5, 227(5): 1251-1264.
[10] 吴红梅, 欧志英. 纳米圆形孔洞SH波散射的复变函数解答[J]. 应用力学学报, 2021, 38( 2): 763-769.
WU Hongmei, OU Zhiying. Complex variable function solution for SH wave scattering in nano circular hole[J]. Chinese Journal of Applied Mechanics, 2021, 38 (2): 763-769.
[11] 刘中宪, 武凤娇, 王冬等. 弹性半空间夹杂群对平面SH波散射的快速多极多域边界元法模拟[J]. 岩土力学, 2017, 38(4): 1154-1163.
LIU Zhongxian, WU Fengjiao, WANG Dong, et al. Multi-domain FMM-IBEM simulation of plane SH wave scattering by inclusions in elastic half-space[J]. Rock and Soil Mechanics, 2017, 38(4): 1154-1163.
[12] 刘殿魁. 各向异性介质中SH波引起的圆孔附近的动应力集中[J]. 力学学报, 1988, 20(5): 443-452.
LIU Diankui. Dynamic stress concentration around a circular cavity by SH wave in an anisotropic media[J]. Acta Mechanica Sinica, 1988, 20(5): 443-452.
[13] 刘殿魁, 袁迎春. 各向异性介质中由SH 波引起的圆孔周围的远场位移[J]. 地震工程与工程振动, 1988, 8(1): 50-59.
LIU Diankui, YUAN Yingchun. Far field displacement around a circular cavity caused by SH wave in an anisotropic medium[J]. Earthquake Engineering and Engineering Vibration, 1988, 8(1): 50-59.
[14] 刘殿魁, 许怡燕. 各向异性介质中SH 波与多个半圆形凹陷地形的相互作用[J]. 力学学报, 1993, 25(1): 93-102.
LIU Diankui, XU Yiyan. Interaction of multiple semi-cylindrical canyons by plane SH wave in anisotropic media[J]. Acta Mechanica Sinica, 1993, 25(1): 93-102.
[15] Liu D K, Han F. Scattering of plane SH wave by noncircular cavity in anisotropic media[J]. Journal of Applied Mechanics, Transactions ASME, 1993, 60(3):769-772.
[16] 陈志刚. 正交各向异性半圆形沉积谷对SH波的散射[J]. 地震工程与工程振动,2016, 1(02): 68-74.
CHEN Zhigang. Scattering of an orthotropic semi-cylindrical alluvial valley by SH waves[J]. Earthquake Engineering and Engineering Vibration, 2016, 1(02):68-74.
[17] Eslami H, Gatmiria B. Two formulations for dynamic response of a cylindrical cavity in crossanisotropic porous media[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2010, 34(4): 331-356.
[18] 钟伟芳, 钱维平. 各向异性体内含任意孔洞对反平面波散射的边界元方法[J]. 固体力学学报, 1990, 11(4): 285-297.
ZHONG Weifang, QIAN Weiping. A boundary element method for calculation the SH wave scattering from arbitrrarily shaped holes in an anisotropic mediun[J]. Acta Mechanica Solida Sinica, 1990, 11(4): 285-297.
[19] 杜修力, 熊建国. 各向异性弹性层中SH波传播的边界元法[J]. 工程力学, 1989, 6(3): 10-18.
DU Xiuli, XIONG Jianguo. Propagation of SH wave in anisotropic midium and the solution by boundary element method[J]. Engineering Mechanices, 1989, 6(3): 10-18.
[20] Martin P A. Scattering by a cavity in an exponentially graded half-space[J]. Journal of Applied Mechanics, 2009, 76: 031009, 4 pages.
[21] Martin P A. Scattering by defects in an exponentially graded layer and misuse of themethod of images[J]. International Journal of Solids Structtures, 2011;48:2164–2166.
[22] Liu Q J, Zhao M J, Zhang C. Antiplane scattering of SH waves by a circular cavity inan exponentially graded half space[J]. International Journal of Engineering Science, 2014, 78: 61–72.
[23] Xu H N, Zhang J W, Yang Z L,et al. Dynamic response of circular cavity and crack in anisotropic elastic half-space by out-plane waves[J]. Mechanics Research Communications, 2018.6, 91: 100-106.