Thermal Vibrations and Localisation Phenomena for Solids with Singularly Perturbed Boundaries

具有奇异摄动边界的固体的热振动和局域化现象

• 批准号: EP/D035082/1
• 负责人: Alexander Movchan
• 金额: $ 18.44万
• 依托单位: University of Liverpool
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FD035082%2F1
• 关键词: Thermal; Vibrations; Localisation; Phenomena; Solids

We plan to study solutions of problems of thermoelasticity in singularly perturbed domains that include subsets of different limit dimensions (multi-structures). A particular feature of the asymptotic approximations used here is the dependence on fast (scaled) variables and hence the presence of boundary layers in the vicinity of singularly perturbed boundaries (e.g. neighbourhoods of junctions regions between elements of a multi-structure). Model fields of the boundary layer type will be studied numerically, and for a certain class of boundary layer formulations analytical solutions are also feasible (for example, some of our model problems can be reduced to functional equations of the Wiener Hopf type). We also plan to use an asymptotic method involving the analysis of Floquet waves in periodic thermoelastic structures to study the influence of a thermal load on transmission and reflection properties of highly porous slabs.

我们计划研究奇异扰动域中热弹性问题的解决方案，其中包括不同极限维度（多结构）的子集。这里使用的渐近近似的一个特殊特征是依赖于快速（缩放）变量，因此在奇异扰动边界附近存在边界层（例如，多结构元素之间的连接区域的邻域）。我们将对边界层类型的模型场进行数值研究，并且对于某一类边界层公式，解析解也是可行的（例如，我们的一些模型问题可以简化为 Wiener Hopf 类型的函数方程）。我们还计划使用渐近方法来分析周期性热弹性结构中的 Floquet 波，以研究热载荷对高多孔板的透射和反射性能的影响。