基于EMT采用FEM研究含裂纹介质中弹性波传播机制

doi:10.13700/j.bh.1001-5965.2014.0663

北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (9): 1686-1692.doi: 10.13700/j.bh.1001-5965.2014.0663

基于EMT采用FEM研究含裂纹介质中弹性波传播机制

刘宁¹, 李敏¹, 陈伟民²

1. 北京航空航天大学航空科学与工程学院, 北京 100191;
2. 中国科学院力学研究所, 北京 100190

收稿日期:2014-10-24 出版日期:2015-09-20 发布日期:2015-09-29
通讯作者: 李敏(1968—),男,教授,湖北天门人,limin@buaa.edu.cn,主要研究方向为结构动力学. E-mail:limin@buaa.edu.cn
作者简介:刘宁(1988—),女,辽宁丹东人,博士研究生,nicolaliu@buaa.edu.cn
基金资助:
国家自然科学基金(11232012,11372320)

Wave propagation in cracked elastic media based on EMT using FEM

LIU Ning¹, LI Min¹, CHEN Weimin²

1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

Received:2014-10-24 Online:2015-09-20 Published:2015-09-29

摘要/Abstract

摘要： 了解和掌握弹性波在含有裂纹介质中的传播规律是开发利用页岩气等非常规油气资源中的关键科学问题.本文基于数值模拟的优点,采用商用有限元软件Nastran模拟弹性波在含裂纹介质中的激发及传播方式,分析了弹性波在该介质中裂纹微结构(密度和纵横比)对弹性波传播动力学特性的依赖程度.结果表明:有限元方法(FEM)可以用于该问题的研究;Hudson等效介质理论(EMT)不适用泊松比近0.5的材料;裂纹密度、纵横比的增大会减小纵波(P波)波速值,以及衰减位移时域响应的首波振幅,且裂纹密度对于该材料的各向异性的影响要远大于纵横比的作用.

关键词: 有限元方法(FEM), Hudson理论, 频率, 裂纹数密度, 横纵比

Abstract: Understanding mechanism of wave propagation in elastic media with cracks is the key scientific issue in exploration and extraction of shale and other unconventional oil and gas resources. Based on the advantages of the numerical simulation, the excitation and propagation of elastic wave in the cracked media were simulated by Nastran, a commercial solver for finite element analysis. Then the dependence of dynamic characteristics of propagation in that kind of media was further analyzed based on the microstructure (crack density, aspect ratio). Some conclusions were obtained as follows. Finite element method (FEM) would be effectively used to study the issue. Hudson's effective medium theory (EMT) could not be applied into materials with Poisson's ratio of nearly 0.5. Increasing crack density and aspect ratio would reduce the primary wave (P wave) velocity, with decaying the displacement amplitude of the P wave in time-domain. Crack density of the medium exposes greater effect on the anisotropy than the aspect ratio.

Key words: finite element method (FEM), Hudson's theory, frequency, crack number density, aspect ratio

中图分类号:

O347.4⁺1

刘宁, 李敏, 陈伟民. 基于EMT采用FEM研究含裂纹介质中弹性波传播机制[J]. 北京航空航天大学学报, 2015, 41(9): 1686-1692.

LIU Ning, LI Min, CHEN Weimin. Wave propagation in cracked elastic media based on EMT using FEM[J]. JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2015, 41(9): 1686-1692.

参考文献

[1] Guéguen Y,Kachanov M.Mechanics of crustal rocks[M].Vienna:Springer,2011:73-125.
[2] Mackenzie J K.The elastic constants of a solid containing spherical holes[J].Proceedings of the Physical Society.Section B.1950,63(1):1.
[3] Eshelby J D.The determination of the elastic field of an ellipsoidal inclusion,and related problems[J].Proceedings of the Royal Society of London.Series A.Mathematical and Physical Sciences,1957,241(1226):376-396.
[4] Bristow J R.Microcracks,and the static and dynamic elastic constants of annealed and heavily cold-worked metals[J].British Journal of Applied Physics,1960,11(2):81.
[5] Walsh J B.The effect of cracks on the compressibility of rock[J].Journal of Geophysical Research,1965,70(2):381-389.
[6] Hudson J A.Overall properties of a cracked solid[C]//Mathematical Proceedings of the Cambridge Philosophical Society.Cambridge:Cambridge University Press,1980,88(2):371-384.
[7] Hudson J A.Seismic wave propagation through material containing partially saturated cracks[J].Geophysical Journal International,1988,92(1):33-37.
[8] Hudson J A.Wave speeds and attenuation of elastic waves in material containing cracks[J].Geophysical Journal International,1981,64(1):133-150.
[9] 曾新吾,韩开锋,张光莹.含裂缝介质中的弹性波传播特性[M].北京:科学出版社,2013:1-5,18-40,98-121.Zeng X W,Han K F,Zhang G Y.Elastic wave propagation characteristics in cracked media[M].Beijing:Science Press,2013:1-5,18-40,98-121(in Chinese).
[10] Courant R.Variational methods for the solution of problems of equilibrium and vibrations[J].Bulletin of American Mathematical Society,1943,49(1):1-23.
[11] Aoki S,Kishimoto K,Kondo H,et al.Elastodynamic analysis of crack by finite element method using singular element[J].International Journal of Fracture,1978,14(1):59-68.
[12] Taylor L M,Chen E,Kuszmaul J S.Microcrack-induced damage accumulation in brittle rock under dynamic loading[J].Computer Methods in Applied Mechanics and Engineering,1986,55(3):301-320.
[13] Ma G W,Hao H,Zhou Y X.Modeling of wave propagation induced by underground explosion[J].Computers and Geotechnics,1998,22(3):283-303.
[14] Garboczi E J,Berryman J G.Elastic moduli of a material containing composite inclusions:Effective medium theory and finite element computations[J].Mechanics of Materials,2001,33(8):455-470.
[15] Grechka V,Kachanov M.Effective elasticity of rocks with closely spaced and intersecting cracks[J].Geophysics,2006,71(3):D85-D91.
[16] Gaede O,Karpfinger F,Jocker J,et al.Comparison between analytical and 3D finite element solutions for borehole stresses in anisotropic elastic rock[J].International Journal of Rock Mechanics and Mining Sciences,2012,51:53-63.
[17] Mavko G,Mukerji T,Dvorkin J.The rock physics handbook:Tools for seismic analysis of porous media[M].Cambridge:Cambridge University Press,2009:21-76.
[18] Thomsen L.Weak elastic anisotropy[J].Geophysics,1986,51(10):1954-1966.
[19] 王勖成.有限单元法[M].北京:清华大学出版社,2003: 468-520.Wang X C.Finite element method[M].Beijing:Tsinghua University Press,2003:468-520(in Chinese).
[20] Liu N,Wang Y,Li M,et al.Nonlinear buckling analyses of a small-radius carbon nanotube[J].Journal of Applied Physics,2014,115(15):154301.

基于EMT采用FEM研究含裂纹介质中弹性波传播机制

Wave propagation in cracked elastic media based on EMT using FEM

PDF (PC)

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

[1]	王岩, 林彬, 东野广恒, 董颖怀, 赵静楠, 张晓峰. 附件化超声振动工作台设计及有限元优化分析[J]. 北京航空航天大学学报, 2019, 45(8): 1589-1596.
[2]	刘小兰, 张献民, 董倩. 飞机滑行下道基动静模量相关分析模型[J]. 北京航空航天大学学报, 2019, 45(4): 778-786.
[3]	王博, 谢军伟, 张晶, 葛佳昂. 基于SD-LCMV算法的FDA平台外干扰抑制[J]. 北京航空航天大学学报, 2019, 45(11): 2247-2256.
[4]	葛佳昂, 谢军伟, 张浩为, 冯晓宇, 张晶. 频率分集阵列对干涉仪的角度欺骗效果[J]. 北京航空航天大学学报, 2019, 45(1): 183-191.
[5]	周睿, 周辉, 桂和利, 董虎, 曹毅. 基于柔性铰链的二自由度微动平台分析及优化[J]. 北京航空航天大学学报, 2018, 44(9): 1982-1990.
[6]	张文旭, 赵文童, 陈涛, 陈亚静. 采用FRM的窄过渡带奇型排列结构改进方法[J]. 北京航空航天大学学报, 2018, 44(5): 951-958.
[7]	冉达, 尹灿斌, 贾鑫. 频率步进SAR虚拟阵列模型成像方法[J]. 北京航空航天大学学报, 2018, 44(1): 82-88.
[8]	张昭建, 谢军伟, 李欣, 盛川, 胡祺勇. 基于FDA-MIMO的距离欺骗干扰鉴别方法[J]. 北京航空航天大学学报, 2017, 43(4): 738-746.
[9]	李欣, 王春阳, 付孝龙, 原慧. 极化通道扩展和盲源分离联合抗移频干扰技术[J]. 北京航空航天大学学报, 2017, 43(4): 731-737.
[10]	赵玉龙, 沈怀荣, 任元. 超流体量子干涉陀螺热驱动方式建模与分析[J]. 北京航空航天大学学报, 2017, 43(12): 2473-2479.
[11]	黄鸯鸯, 王保良, 冀海峰, 黄志尧, 李海青. 基于Lamb波气体传感器的数据采集仪[J]. 北京航空航天大学学报, 2017, 43(11): 2216-2223.
[12]	王野, 谭超, 董峰. 多激励频率模式的磁感应层析成像系统[J]. 北京航空航天大学学报, 2017, 43(11): 2331-2337.
[13]	付孝龙, 白渭雄, 李欣, 原慧, 陈津津. 基于多普勒频率差的拖曳式诱饵干扰检测[J]. 北京航空航天大学学报, 2017, 43(10): 2081-2088.
[14]	周龙健, 罗景青. 低秩条件下双星TDOA和FDOA无源定位算法[J]. 北京航空航天大学学报, 2017, 43(10): 2040-2046.
[15]	周正干, 贺鹏飞, 赵翰学, 范瑾. 钛合金蜂窝结构蒙皮脱焊缺陷锁相红外热成像检测[J]. 北京航空航天大学学报, 2016, 42(9): 1795-1802.