标题： 关于晶格中的共振波 显示英文标题

标题： On Resonant Waves in Lattices

摘要： 对在二维周期无限晶格中传播的共振波进行数学建模。 考虑矩形单元、三角形单元和六边形单元晶格。 确定稳态问题的特征值（此处为特征频率），并描述自由波的色散特性。 我们表明，模型的频率谱在通带/禁带边界以及通带内部都存在多个共振点。 研究具有局部单色源的边界值问题，并揭示共振波的特性。 将渐近解与计算机模拟的结果进行比较。 特别关注共振频率下的线局域原始波形以及共振激励下的波束现象。 显示英文摘要

摘要： Mathematical modeling of resonant waves propagating in 2D periodic infinite lattices is conducted. Rectangular-cell, triangular-cell and hexagonal-cell lattices are considered. Eigenvalues (here eigenfrequencies) of steady-state problems are determined, and dispersion properties of free waves are described. We show that the frequency spectra of the models possess several resonant points located both at the boundary of pass/stop bands and in the interior of a pass band. Boundary value problems with a local monochromatic source are explored, and peculiarities of resonant waves are revealed. Asymptotic solutions are compared with the results of computer simulation. Special attention is given to line-localized primitive waveforms at the resonance frequencies and to the wave beaming phenomena at a resonant excitation.