变曲率及阵列纳米尺度夹杂附近的弹性波散射

When elastic waves propagate in the solid, scattering occurs around the inclusions. As a result of scattering, the stresses near the inclusions are different which is the phenomenon known as dynamic stress concentration. For nanosized inclusions,interface and surface have significant effects on the physical and mechanical properties of solids, due to the increasing ratio of interface/surface area to volume.Base on the interface/surface elasticity theory and classical elasticity theory, using the displacement potential method and wave functions expansion method, this project studies the scattering of elastic waves around nanoscaled inclusions for different scape and arrangement. When incident waves with different frequencies, for different interface/surface parameter,elastic constants of inclusions and the distance between inclusions, the dynamic stress concention around the inclusions and the scattering cross section are caculated. This will provide the theoretical basis for the dynamic analysis of nano materials and nano components.

弹性波在固体中传播时，会在固体中的夹杂周围产生弹性波散射现象，从而引起动应力集中。对纳米尺度夹杂而言，夹杂尺度小，其比表面积显著增加，表面能对材料物理性质和力学性质的影响变得非常显著。本项目拟在表面弹性理论和经典弹性理论的基础上，用位移势函数法和波函数展开法，以及弹性波的多重散射理论，研究不同形状和不同阵列纳米尺度夹杂附近的弹性波散射及其诱发的动应力集中问题。研究弹性波以不同频率入射时，不同表面参数、夹杂材料的弹性常数和夹杂间距离对纳米尺度夹杂周围动应力集中和散射通量的影响。为研究微纳米材料及其构件的动力学问题提供理论依据。

弹性波在固体中传播时，在固体中存在的夹杂（孔洞）等缺陷周围会发生弹性波散射的现象，从而引起动应力集中。当夹杂（孔洞）的尺寸缩小到纳米尺度时，比表面积显著增加，表面能的影响变得非常重要。项目以表面弹性理论和经典弹性理论为基础，系统的研究了界/表面效应对弹性波散射诱发的纳米尺度夹杂周围动应力集中的影响，得到了创新性结论，主要包含以下几方面的内容：.基于表面弹性理论和经典弹性理论，用位移势函数法、波函数展开法和弹性波的多重散射理论，求得了无限大介质中一组纳米圆柱孔洞周围由弹性波诱发的应力场；求得了弹性波诱发的表面自由的半无限大介质中纳米圆柱孔洞附近的应力场。分析了表面效应对孔洞周围动应力集中的影响。结果表明，纳米圆柱孔洞周围的动应力集中不仅和表面常数有关，而且和孔洞之间的距离以及孔洞和自由表面之间的距离有关。.本项目的研究结果为纳米材料及其构件和轻质多孔材料的动力学行为分析提供了理论依据。