Thermal Vibrations and Localisation Phenomena for Solids with Singularly Perturbed Boundaries

我们计划研究包含不同极限维度(多结构)的子集的奇异摄动区域中热弹性问题的解。这里使用的渐近近似的一个特殊特征是对快速(缩放)变量的依赖，因此在奇异扰动边界(例如，多结构元素之间的结合区的邻域)附近存在边界层。边界层类型的模型场将被数值研究，对于某类边界层公式，解析解也是可行的(例如，我们的一些模型问题可以归结为Wiener Hopf类型的函数方程)。我们还计划使用一种分析周期热弹性结构中Floquit波的渐近方法来研究热载荷对高孔板的透射率和反射率的影响。

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.