Abstract
Complex function method and multi-polar coordinate transformation technology are used here to study scattering of circular cavity in right-angle planar space to SH-wave with out-of-plane loading on the horizontal straight boundary. At first, Green function of right-angle planar space which has no circular cavity is constructed; then the scattering solution which satisfies the free stress conditions of the two right-angle boundaries with the circular cavity existing in the space is formulated. Therefore, the total displacement field can be constructed using overlapping principle. An infinite algebraic equations of unknown coefficients existing in the scattering solution field can be gained using multi-polar coordinate and the free stress condition at the boundary of the circular cavity. It can be solved by using limit items in the infinite series which can give a high computation precision. An example is given to illustrate the variations of the tangential stress at the boundary of the circular cavity due to different dimensionless wave numbers, the location of the circular cavity, the loading center and the distributing range of the out-of-plane loading. The results show the efficiency and effectiveness of the mothod introduced here.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Liu Diankui, Gai Bingzheng, Tao Guiyuan. On dynamic stress concentration in the neighbour-hood of a cavity [J]. Acta Mechanica Sinica, 1981, 65–77 (in Chinese).
Vardoul Akis I, Georgiadis H G. SH surface waves in a homogeneous gradient elastic half-space with surface energy[J]. Journal of Elasticity, 1997, 47(2):147–165.
Emets V F, Kunets Ya I, Matus V V. Scattering of SH waves by an elastic thin walled rigidly-supported inclusion[J]. Archive of Applied Mechanics, 2004, 73(11–12):769–780.
Liu Diankui, Liu Hongwei. Scattering and dynamic stress concentration of SH-wave by interface circular hole[J]. Acta Mechanica Sinica, 1998, 30(5):597–604 (in Chinese).
Liu Diankui, Xu Yiyan. Interaction of multiple semi-cylindrical canyons by plane SH-wave in anisotropic media[J]. Acta Mechanica Sinica, 1993, 25(1):94–102 (in Chinese).
Xu Yiyan, Han Feng. Scattering of several half-circular canyon to SH-wave[J]. Earthquake Engineering and Engineering Vibration, 1992, 12(2):12–17 (in Chinese).
Han Feng, Liu Diankui. Scattering of plane SH-waves on semi-canyon topography of arbitrary shape with lining in anisotropic media[J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(8):753–761.
Liu Diankui, Tian Jiayong. Scattering and dynamic stress concentration of SH-wave by interface cylindrical elastic inclusion[J]. Explosion and Shock Waves, 1991, 9(2):115–123 (in Chinese).
Cui Zhigang, Zou Yongchao, Liu Diankui. Scattering of plane SH-wave by a cylindrical hill of circular-arc cross section[J]. Earthquake Engineering and Engineering Vibration, 1998, 18(4):8–14 (in Chinese).
Cao Xinrong, Song Tianshu, Liu Diankui. Scattering of plane SH-wave by a cylindrical hill of arbitrary shape[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(9):1082–1089.
Chen Zhigang, Liu Diankui. Green function in elastic half space impacted by out-place harmonic line source loading at horizontal surface[J]. Journal of Harbin Engineering University, 2002, 23(4):103–109 (in Chinese).
Shi Shouxia. Scattering of SH-wave by the structure surface with multiple semi-cylindrical medium inclusion[J]. Acta Aeronautical Et Astronautica Sinica, 2001, 22(1):19–23 (in Chinese).
Fang Yingguang. Series solution for scattering of plane SH-waves by multiple shallow circular-arc canyons[J]. Applied Mathematics and Mechanics (English Edition), 1995, 16(7):657–666.
Wang Yuesheng, Wang Duo. Diffraction of SH-waves by a circular cavity with a partially debounded liner[J]. Acta Mechanica Sinica, 1994, 26(4):462–469 (in Chinese).
Yuan Xiaoming, Liao Zhenpeng. Scattering of plane SH waves by a cylindrical hill of circular-arc cross section[J]. Earthquake Engineering and Engineering Vibration, 1996, 16(2):1–13 (in Chinese).
Yuan Xiaoming, Liao Zhenpeng. Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross section[J]. South China Journal of Seismology, 1995, 15(2):1–8 (in Chinese).
Liang Jianwen, Zhang Yushan, Gu Xiaolu. Scattering of plane SH waves by a circular-arc layered canyon[J]. Journal of Vibration Engineering, 2003, 16(2):158–165 (in Chinese).
Yuan Xiaoming. Effect of circular underground inclusion on surface motion under incident plane SH waves[J]. Acta Geophysica Sinica, 1996, 39(3):373–381 (in Chinese).
Fang Yingguang. Scattering of plane SH-waves by multiple circular arc valleys at the two-dimensional surface of the earth[J]. Earthquake Engineering and Engineering Vibration, 1995, 15(1):85–91 (in Chinese).
He Zhongyi, Fan Hongming, Liu Youjun. Scattering of SH-wave by an interface cavity[J]. Acta Mechanica Sinica, 2002, 34(1):68–75 (in Chinese).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by CHEN Yu-shu
Rights and permissions
About this article
Cite this article
Shi, Wp., Liu, Dk., Song, Yt. et al. Scattering of circular cavity in right-angle planar space to steady SH-wave. Appl Math Mech 27, 1619–1626 (2006). https://doi.org/10.1007/s10483-006-1204-1
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10483-006-1204-1