Pupyrev Pavel D, Lomonosov Alexey M, Nikodijevic Aleksandar, Mayer Andreas P
General Physics Institute, RAS, Moscow, Russian Federation; HS Offenburg - University of Applied Sciences, 77723 Gengenbach, Germany.
HS Offenburg - University of Applied Sciences, 77723 Gengenbach, Germany.
Ultrasonics. 2016 Sep;71:278-287. doi: 10.1016/j.ultras.2016.06.016. Epub 2016 Jun 28.
The existence of acoustic waves with displacements localized at the tip of an isotropic elastic wedge was rigorously proven by Kamotskii, Zavorokhin and Nazarov. This proof, which is based on a variational approach, is extended to rectangular anisotropic wedges. For two high-symmetry configurations of rectangular edges in elastic media with tetragonal symmetry, a criterion is derived that allows identifying the boundary between the regions of existence for wedge modes of even and odd symmetry in regions of parameter space, where even- and odd-symmetry modes do not exist simultaneously. Furthermore, rectangular edges with non-equivalent surfaces are analyzed, and it is shown that at rectangular edges of cubic elastic media with one (110) surface and one (001) surface, a tip-localized guided wave always exists, apart from special cases that are characterized.
卡莫茨基、扎沃罗欣和纳扎罗夫严格证明了位移局限于各向同性弹性楔尖端的声波的存在。基于变分法的这一证明被扩展到矩形各向异性楔。对于具有四方对称性的弹性介质中矩形边缘的两种高对称构型，推导了一个准则，该准则允许在参数空间区域中识别偶数和奇数对称楔模式的存在区域之间的边界，其中偶数和奇数对称模式不同时存在。此外，对具有不等效表面的矩形边缘进行了分析，结果表明，在具有一个（110）表面和一个（001）表面的立方弹性介质的矩形边缘处，除了所表征的特殊情况外，总是存在尖端局域导波。
