Maksimov Dmitrii N, Sadreev Almas F
Institute of Physics, Academy of Sciences, 660036 Krasnoyarsk, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jul;74(1 Pt 2):016201. doi: 10.1103/PhysRevE.74.016201. Epub 2006 Jul 6.
We consider numerically the L-, T-, and X-shaped elastic waveguides with the Dirichlet boundary conditions for in-plane deformations (displacements) which obey the vectorial Navier-Cauchy equation. In the X-shaped waveguide we show the existence of a doubly degenerate bound state with frequency below the first symmetrical cutoff frequency, which belongs to the two-dimensional irreducible representation E of symmetry group C(4upsilon). Moreover the next bound state is below the next antisymmetric cutoff frequency. This bound state belongs to the irreducible representation A2. The T-shaped waveguide has only one bound state while the L-shaped one has no bound states.
我们对具有平面内变形（位移）的狄利克雷边界条件且服从矢量纳维 - 柯西方程的L形、T形和X形弹性波导进行了数值研究。在X形波导中，我们展示了存在一个频率低于第一个对称截止频率的双重简并束缚态，它属于对称群C(4υ)的二维不可约表示E。此外，下一个束缚态低于下一个反对称截止频率。这个束缚态属于不可约表示A2。T形波导只有一个束缚态，而L形波导没有束缚态。
