通过周期性空洞界面的有效弹性波传输
Effective elastic wave transmission through a periodically voided interface
AI总结：
本文推导了周期性空洞薄层分离两个均匀体区域的弹性波方程有效界面条件，通过同时取薄层周期性和厚度趋于零的极限，采用展开法处理薄孔洞域，考虑三种不同材料参数尺度化情况，得出不同类型的界面条件，并在临界 regime 中引入微观变量。
摘要：
本文推导了周期性空洞薄层分离两个均匀体区域的弹性波方程有效界面条件，通过同时取薄层周期性和厚度趋于零的极限，采用展开法处理薄孔洞域。我们考虑了三种不同材料参数尺度化情况，每种情况对应不同的界面条件，并需要求解依赖于尺度的单元问题。根据不同的尺度，所得有效模型产生膜方程或Kirchhoff-Love板方程。在减小刚度的临界 regime 中，界面方程还依赖于微观变量。通过选择适当的单元问题，此方程可以改写为体域之间的有效界面条件。
英文摘要：
Effective interface conditions for a periodically voided thin layer separating two homogeneous bulk regions are derived for the elastic wave equation by taking the simultaneous limit of vanishing layer periodicity and layer thickness. The limit problems are obtained using the unfolding method for thin perforated domains. We consider three different scalings of the material parameters in the layer that characterise its stiffness, each leading to a distinct type of interface condition and requiring the solution of scaling-dependent cell problems. Depending on the scaling, the resulting effective model yields either a membrane equation or a Kirchhoff-Love plate equation. In the critical regime of reduced stiffness, the interface equation additionally depends on the microscopic variable. By selecting appropriate cell problems, this equation can be reformulated as an effective interface condition between the bulk domains.
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