周期分布不规则体对弹性波的二维散射  

Two-dimensional scattering of elastic waves by periodic distribution irregularities in an elastic full space

作　　者：巴振宁[1,2] 高旭 梁建文[1,2] BA Zhenning;GAO Xu;LIANG Jianwen(School of Civil Engineering,Tianjin University,Tianjin 300072,China;Key Laboratory of Coast Civil Structure Safety,Ministry of Education,Tianjin University,Tianjin 300072,China)

机构地区：[1]天津大学建筑工程学院,天津300072 [2]天津大学,滨海土木工程结构与新材料教育部重点实验室,天津300072

出　　处：《振动与冲击》2020年第14期201-213,共13页Journal of Vibration and Shock

基　　金：国家自然科学基金(51778413,51578373)。

摘　　要：建立了一种基于均布线载动力格林函数的周期间接边界元方法(PIBEM),进而研究了全空间中周期分布不规则体对弹性波的散射问题。方法利用平面波入射下,各不规则体周围波场频域内仅相差一个相位的特征,仅需针对其中一个不规则体进行离散和求解,即可求得问题的解;相对于选取有限多个不规则体进行近似求解的方法,该方法具有较高精度的同时,最大限度的降低了求解自由度;在对方法正确性验证的基础上,以全空间中空洞和加塞两种模型为例开展了数值计算分析,重点探讨了空洞形状、空洞间距和加塞刚度等参数对减振效应的影响。数值分析结果表明:周期分布空洞与多个空洞的位移幅值具有差异,且频率低时差异更为显著;三种形状空洞中,周期分布圆形空洞减振效果最佳,周期分布三角形空洞减振效果最差;周期分布加塞与周期分布空洞减振原理不同,加塞通过消耗地震波的能量减振,而空洞通过阻隔地震波减振;周期分布软加塞的消能减振效果优于周期分布硬加塞。A periodic indirect boundary element method(PIBEM) based on the dynamic Green’s functions of uniformly distributed loads was used to study the scattering and diffraction of plane P-waves and SV-waves by periodically distributed irregular bodies in a full-space. By virtue of the fact that the dynamic responses around each of the canyons along the x-axis has the particular feature of repeating themselves with a certain delay of phase in frequency domain, the effort can be reduced to discretize and solve only a single irregular body. Compared with the method of truncating a finite number of irregular bodies for approximate solution, the method proposed in this paper has the advantages of higher precision and greater memory reduction. The accuracy of the method was verified by comparing its degenerated results with published results. Numerical calculations were performed for the periodically distributed cavities and cavities with media in frequency domain and the influences of the cavity shape, spacing and stiffness of media on the vibration-isolating effect were discussed. The numerical results show that the displacement amplitude in the case of periodically distributed cavities is different from that in the case of multiple cavities, and the difference is significant at low frequency, indicating that it is difficult to obtain accurate solutions by truncating a finite number of cavities. Among three kinds of shaped cavities, the periodically distributed circular cavities have the best vibration-isolating effect, and the periodically distributed triangular cavities have the worst. The principle of periodically distributed cavities is different from that of periodically distributed cavities with media, the later consumes the energy of seismic waves to reduce earthquake effect, while the former blocks seismic waves to reduce earthquake. The vibration-isolating effect of periodically distributed cavities with flexible media is better than that of periodically distributed cavities with rigid media.

关 键 词：周期分布不规则体 格林函数 P波和SV波 散射 

分 类 号：P315.3[天文地球—地震学]