An advanced direct half-plane time-domain boundary element method (BEM) was applied to obtain the seismic response of a linear elastic irregular surface including periodically distributed semi-sine shaped valleys subjected to propagating obliquely incident plane SH waves. After developing the method for complex multiple surface topographies, some verification examples were solved and compared with those of the published works. Then, the transient response of a rough surface with 2–16 semi-sine shaped valleys was determined as synthetic seismograms. In this regard, the depth ratio of the valleys was sensitized. Finally, amplification patterns of the surface were presented in some cases. The results showed that the method was able to analyze the multipart models in the time-domain. Moreover, the response of the sinusoidal corrugated surfaces was very effective against seismic waves in forming different patterns. The method was recommended to researchers for transient analysis of complex engineering structures and composite materials in nanoscale.

中文翻译：

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周期性分布的半正弦波谷对不规则表面的瞬态响应：入射 SH 波

应用先进的直接半平面时域边界元法（BEM）获得线性弹性不规则表面的地震响应，该表面包括周期性分布的半正弦形谷地，其受到传播的倾斜入射平面SH波的影响。在开发了复杂多表面形貌的方法后，解决了一些验证实例，并与已发表的作品进行了比较。然后，将具有 2-16 个半正弦波谷的粗糙表面的瞬态响应确定为合成地震图。在这方面，谷的深度比是敏感的。最后，在某些情况下呈现了表面的放大模式。结果表明，该方法能够对多部分模型进行时域分析。而且，正弦波纹表面的响应在形成不同的模式时对地震波非常有效。该方法被推荐给研究人员用于纳米级复杂工程结构和复合材料的瞬态分析。