工程力学 ›› 2018, Vol. 35 ›› Issue (7): 7-17,23.doi: 10.6052/j.issn.1000-4750.2017.03.0181

• 基本方法 • 上一篇    下一篇

任意多个凸起地形对平面P波的散射

巴振宁1,2, 彭琳3, 梁建文1,2, 黄棣旸1   

  1. 1. 天津大学土木系, 天津 300072;
    2. 滨海土木工程结构与新材料教育部重点实验室, 天津 300072;
    3. 中国建筑股份有限公司技术中心, 北京 101300
  • 收稿日期:2017-03-08 修回日期:2018-03-27 出版日期:2018-07-25 发布日期:2018-07-26
  • 通讯作者: 梁建文(1965-),男,河北人,教授,博士,主要从事地震工程研究(E-mail:liang@tju.edu.cn) E-mail:liang@tju.edu.cn)
  • 作者简介:巴振宁(1980-),男,山东东营人,教授,博士,主要从事地震工程研究(E-mail:bazhenning_001@163.com);彭琳(1993-),女,河北人,硕士生,主要从事地震工程研究(E-mail:penglin_sunny@163.com);黄棣旸(1993-),男,江苏人,硕士生,主要从事地震工程研究(E-mail:huangdiyang_001@163.com).
  • 基金资助:
    国家自然科学基金项目(51778413,51578373)

SCATTER AND DIFFRACTION OF ARBITRARY NUMBER OF HILLS FOR INCIDENT PLANE P-WAVES

BA Zhen-ning1,2, PENG Lin3, LIANG Jian-wen1,2, HUANG Di-yang1   

  1. 1. Department of Civil Engineering, Tianjin University, Tianjin 300072, China;
    2. Key Laboratory of Coast Civil Structure Safety(Tianjin University), Ministry of Education Tianjin 300072, China;
    3. China State Construction Technical Center, Beijing 101300, China
  • Received:2017-03-08 Revised:2018-03-27 Online:2018-07-25 Published:2018-07-26

摘要: 结合"分区契合"技术,采用间接边界元方法研究了任意多个凸起地形对平面P波的散射问题。求解中将模型分解为开口层状半空间域和多个凸起闭合域,同时将波场分解为自由波场和散射波场。自由波场由直接刚度法求得,而开口域和闭合域内的散射波场则通过在相应的边界上施加虚拟均布荷载,求解动力格林函数来模拟,虚拟荷载密度通过引入边界条件确定。该文通过与已有结果的比较验证了方法的正确性,进而开展数值计算,研究了两侧凸起高度、凸起间距和凸起个数对中间凸起及附近地表位移幅值的影响。数值结果表明:凸起间存在动力相互作用,使得多个凸起情况位移幅值显著大于单一凸起情况,多个凸起与单一凸起对应的位移幅值及放大谱均存在显著差异;两侧凸起的高度和凸起间距的改变,均使得凸起间动力相互作用机制发生了改变,进而改变了放大谱的峰值以及峰值频率。凸起个数对凸起间动力相互作用机制影响较小,不同凸起个数情况对应的放大谱峰值频率非常接近;两侧凸起高度的增大、凸起间距的减小以及凸起个数的增多,会使得凸起间动力相互作用进一步加强,位移幅值较大且空间分布更为复杂。

关键词: 间接边界元法, 平面P波, 散射, 多个凸起地形, 动力相互作用

Abstract: The diffraction of plane P waves on multiple hills of an arbitrary number is studied using an indirect boundary element method (IBEM), combined with the technology of ‘conjunction’. The model is divided into an open layered half-space region and multiple independent closed regions. Wave fields are classified as free fields and scattered fields. The free field response can be solved by the direct stiffness method, and the diffraction response of the open layered half-space region and closed regions can be simulated by the Green's function of fictitious distributed loads acting on corresponding boundaries. And the densities of the distributed loads are determined by solving the algebraic system based on boundary conditions. The validity of the method is confirmed by the comparison with published results. Then numerical analyses are performed by multiple hills topography in the cases of different heights, different distances and different numbers. The results show that the surface displacement of multiple hills is significantly bigger than those of a single hill because of the dynamic interaction among hills, making the surface displacement and spectrum amplification of multiple hills obviously different from those of a single hill. The variation of heights and distances of hills on both sides would lead to the changes in the dynamic interaction mechanism within hills, which alter the peak and peak-period amplification of spectrum furthermore. Increases in heights and numbers of hills on both sides, as well as decreases in distances from each other will result in a more intensive dynamic interaction, a bigger displacement and a more complex spatial distribution.

Key words: Indirect boundary element method (IBEM), plane P waves, diffraction, multiple hills, dynamic interaction

中图分类号: 

  • TU435
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