[1]陈志刚.应用最小二乘法求解平面P波在孔洞上的散射[J].地震工程与工程振动,2019,39(06):106-112.[doi:10.13197/j.eeev.2019.06.106.chenzg.015]
 CHEN Zhigang.Application of least square method to solve the scattering of plane P-wave on a cavity[J].EARTHQUAKE ENGINEERING AND ENGINEERING DYNAMICS,2019,39(06):106-112.[doi:10.13197/j.eeev.2019.06.106.chenzg.015]
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应用最小二乘法求解平面P波在孔洞上的散射
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《地震工程与工程振动》[ISSN:/CN:]

卷:
39
期数:
2019年06
页码:
106-112
栏目:
论文
出版日期:
2019-12-31

文章信息/Info

Title:
Application of least square method to solve the scattering of plane P-wave on a cavity
作者:
陈志刚12
1. 暨南大学 力学与建筑工程学院, 广东 广州 510632;
2. 暨南大学 重大工程灾害与控制教育部重点实验室, 广东 广州 510632
Author(s):
CHEN Zhigang12
1. School of Mechanics and Construction Engineering, Jinan University, Guangzhou 510632, China;
2. MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University, Guangzhou 510632, China
关键词:
平面P波动应力集中系数孔洞最小二乘法复变函数法
Keywords:
plane P-wavedynamic stress concentration factorscavityleast square methodcomplex function method
分类号:
O347.4;P315.3
DOI:
10.13197/j.eeev.2019.06.106.chenzg.015
摘要:
弹性波在孔洞上的散射问题可采用复变函数方法求解,用含有待定系数的"域函数"表示散射波的位移势函数,如何准确地求解该待定系数是获得问题解答的关键。本文根据孔洞边缘的径向和切向应力为零的边界条件用最小二乘法建立求解待定系数的线性方程组,得到有限项系数的近似解。通过圆孔、椭圆孔和方孔的数值算例,分析了P波作用下不同形状孔洞边缘的动应力集中系数的特征,讨论了孔边的径向和切向应力计算误差与待定系数项数的关系。计算结果表明,采用最小二乘法求解散射波的待定系数,能够获得满足一定精度要求的孔附近动应力集中系数的解答。
Abstract:
The scattering problem ofelastic waves on a cavity can be solved by complex function method.The "domain function" containing the undetermined coefficient is used to represent the displacement potential function of the scattered wave. How to solve the undetermined coefficientaccurately is the key to obtain the solution.In this paper, based on the boundary condition of the radial stress at the boundary of the cavity is zero, a set of linear equations for solving the undetermined coefficients are established by the least squares method, and the approximate solution of the finite term coefficients is obtained.Through numerical examples of circular, elliptical and square cavities, the characteristics of dynamic stress concentration factorsat the boundary of cavities with different shapes under P-wave are analyzed. The relationship between the accuracy of radial and tangential stress calculation at the cavity boundary and the number of undetermined coefficients is discussed.The calculation results show that the least square method can be introduced to solve the undetermined coefficients of the scattered wave, and the solution of the dynamic stress concentration factors near the cavity that meets certain accuracy requirements can be obtained.

参考文献/References:

[1] 胡聿贤.地震工程学[M].2版.北京:地震出版社,2006:222-244. HU Yuxian. Earthquake engineering[M]. 2nd ed. Beijing:Seismological Press, 2006:222-244.(in Chinese)
[2] 夏禾.交通环境振动[M].北京:科学出版社,2010:253-259. XIA He. Traffic induced environmental vibrations and controls[M]. Beijing:Science Press,2010:253-259.(in Chinese)
[3] Subhendu K. Datta and Arvind H. Shah.Elastic waves in composite media and structures:with applications to ultrasonic nondestructive evaluation[M]. Boca Raton:CRC Press, 2009:224-225.
[4] 田林, 徐则民, 张家明. 局部地形下入射波散射效应对场地地震响应的影响[J]. 地球物理学进展, 2012,27(1):122-130. Tian Lin, Xu Zemin, Zhang Jiaming. Seismic response for local landform subjected to scattering of incident wave[J]. Progress in Geophysics, 2012,27(1):122-130.(in Chinese)
[5] 张家明, 徐则民, 田林, 等.局部地形下入射波散射效应对地震动影响解析解研究进展[J]. 中国地震, 2012,28(3):231-244. ZHANG Jiaming, XU Zemin, TIAN Lin, et al. A review of analytical solution of scattering effect of incident wave by local topography on ground motion[J]. Earthquake Research in China, 2012,28(3):231-244.(in Chinese)
[6] 刘殿魁,林宏.2003.浅埋的圆柱形孔洞对SH波的散射与地震动[J].爆炸与冲击,2003,23(1):6-12. LIU Diankui, LIN Hong. Scattering of SH waves by a shallow buried cylindrical cavity and the ground motion[J]. Explosion and Shock Waves,2003,23(1):6-12.(in Chinese)
[7] 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.(in Chinese)
[8] Lee V W,Trifunac M D. Response of tunnels to incident SH-wave[J].Engineering Mechanics Div. ASCE,1979,105(4):643-659.
[9] Lee V W,Karl J. Diffraction of SV waves by underground circular cylindrical cavities[J]. Soil Dynamics and Earthquake Engineering, 1992,11(8):445-456.
[10] LIANG Jianwen,ZHAO Hao,Lee V W. A series solution for surface motion amplification due to underground twin tunnels:incident SV waves[J]. Earthquake Engineering and Engineering Vibration, 2003,2(2):289-298.
[11] PaoYih-Hsingand MowChao-Chow, Diffraction of elastic waves and dynamic stress concentrations[M]. New York:Crane Russak, 1971:208-304,401-467.
[12] 黎在良,刘殿魁. 固体中的波[M].北京:科学出版社,1995:286-318,323-338. LI Zailiang,LIU Diankui. Waves in solids[M]. Beijing:Science Press, 1995:286-318,323-338.(in Chinese)
[13] LIU Diankui, GAI.Bingzheng, TAO Guiyuan. Applications of the method of complex function to dynamic stress concentration[J]. Wave motion, 1982(4):293-304.
[14] 刘殿魁,盖秉政,陶贵源. 论孔附近的动应力集中[J].地震工程与工程振动,1980,试刊1期:97-110. LIU Diankui, GAI Bingzheng, TAO Guiyuan. On dynamic stress concentration in the neighbourhood of a cavity[J].Earthquake Engineering and Engineering Vibration, 1980, Trial Issue 1:97-110.

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备注/Memo

备注/Memo:
收稿日期:2019-08-15;改回日期:2019-10-11。
基金项目:暨南大学"重大工程灾害与控制"教育部重点实验室项目
作者简介:陈志刚(1965-),男,副教授,博士,主要从事弹性波动理论和结构动力分析研究.E-mail:czgjnu@163.com
更新日期/Last Update: 1900-01-01