This paper presents a closed-form analytical solution for the dynamic response of two independent SDOF oscillators standing on one flexible foundation embedded in an elastic half-space and excited by plane SH waves. The solution is obtained by the wave function expansion method and is verified by comparison with the results of the special cases of a rigid foundation and the published research result of a flexible foundation. The model is utilized to investigate how the foundation stiffness influences the system response. The results show that there will be a significant interaction between the two independent structures on one flexible foundation and the intensity of the interaction is mainly dependent on foundation stiffness and structural stiffness. For a system with more flexible foundation, strong interaction will exist between the two structures; larger structural stiffness will also lead to a strong interaction between the two structures. When the structural mass and the structural stiffness are all larger, the flexible foundation cannot be treated as a rigid foundation even if the foundation stiffness is many times larger than that of soil. This model may be useful to get insight into the effects of foundation flexibility on the interaction of two independent structures standing on one flexible foundation.

中文翻译：

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嵌入半空间的柔性基础支持的两个独立单自由度振荡器的动态相互作用：入射平面 SH 波的封闭式解析解

本文提出了一种封闭形式的解析解，用于两个独立的单自由度振荡器的动态响应，该振荡器位于一个嵌入弹性半空间并由平面 SH 波激发的柔性基础上。该解采用波函数展开法得到，并与刚性地基特例结果和已发表的柔性地基研究结果进行了对比验证。该模型用于研究基础刚度如何影响系统响应。结果表明，在一个柔性基础上，两个独立结构之间会存在显着的相互作用，相互作用的强度主要取决于基础刚度和结构刚度。对于基础更灵活的系统，两种结构之间将存在强烈的相互作用；较大的结构刚度也将导致两个结构之间的强烈相互作用。当结构质量和结构刚度都较大时，即使地基刚度比土的刚度大很多倍，柔性地基也不能被视为刚性地基。该模型可能有助于深入了解基础柔性对站在一个柔性基础上的两个独立结构的相互作用的影响。