论文标题
曲率对较低维弹性材料中波动波的传播的影响
The effects of curvature on the propagation of undulatory waves in lower dimensional elastic materials
论文作者
论文摘要
较低维弹性结构的力学在很大程度上取决于其无压力状态的几何形状。弹性变形分离为平面内拉伸和降低平面外弯曲变形。对于具有无应力状态的弹性结构，这两种弹性模式在线性弹性中耦合。我们研究了该曲率诱导的耦合对较低维弹性结构中波传播的影响，重点是最简单的示例 - 弯曲的弹性杆。我们发现，在存在有限曲率的情况下，波的分散关系被掩盖。弯曲模式与杆曲率成比例的频率低于杆的曲率。通过研究均匀曲率区域的波动性波的散射，我们发现与弯曲区域隧道在弯曲区域通过转换为压缩波的间隙相关的频率的波动波的频率。这些结果应直接适用于许多弯曲棒状弹性固体（包括碳纳米管和生物聚合物丝）中声子的光谱和空间分布。
The mechanics of lower dimensional elastic structures depends strongly on the geometry of their stress-free state. Elastic deformations separate into in-plane stretching and lower energy out-of-plane bending deformations. For elastic structures with a curved stress-free state, these two elastic modes are coupled within linear elasticity. We investigate the effect of that curvature-induced coupling on wave propagation in lower dimensional elastic structures, focusing on the simplest example -- a curved elastic rod. We find that the dispersion relation of the waves becomes gapped in the presence of finite curvature; bending modes are absent below a frequency proportional to the curvature of the rod. By studying the scattering of undulatory waves off regions of uniform curvature, we find that undulatory waves with frequencies in the gap associated with the curved region tunnel through that curved region via conversion into compression waves. These results should be directly applicable to the spectrum and spatial distribution of phonon modes in a number of curved rod-like elastic solids, including carbon nanotubes and biopolymer filaments.
