论文标题
弹性波从单个和双重的周期性缺陷中散射
Elastic Wave Scattering off a Single and Double Array of Periodic Defects
论文作者
论文摘要
弹性波散射出薄圆柱缺陷的周期性单和双阵列被认为是各向同性材料的。通过Lippmann-Schwinger形式主义获得散射矩阵的分析表达，并使用Schloemilch系列在长波长极限中进行分析，以便获得散射基质极线的显式表达式。然后使用后者证明，对于物理和几何参数空间中的特定曲线，散射由共振支配，并且在剪切模式平行于圆柱体的剪切模式下的共振宽度具有参数空间的全球最小值。在相似的光子或声学系统中未观察到这一特征。对于双阵列，研究了由于正常牵引边界条件而导致的剪切和压缩模式的共振。这些共振对物理和几何参数的宽度的分析依赖性被利用以证明存在消失宽度的共振存在，被称为连续体（BSC）中的结合状态。 BSC的光谱特征是根据Bloch相和弹性模式的组速度明确发现的。
Elastic waves scattering off a periodic single and double array of thin cylindrical defects is considered for isotropic materials. An analytical expression for the scattering matrix is obtained by means of the Lippmann-Schwinger formalism and analyzed in the long wavelength limit using Schloemilch series in order to obtain explicit expressions for the poles of the scattering matrix. The latter is then used to prove that for a specific curve in the space of physical and geometric parameters, the scattering is dominated by resonances, and the width of the resonances in the shear mode parallel to the cylinders has a global minimum in parameter space. This a feature is not observed in similar photonic or acoustic systems. The resonances in shear and compression modes that are coupled in the plane perpendicular to the cylinders due to the normal traction boundary condition are studied for the double array. The analytical dependence of the width of these resonances on physical and geometrical parameters is exploited to prove the existence of resonances with the vanishing width, known as Bound States in the Continuum (BSC). Spectral characteristics of BSC are explicitly found in terms of the Bloch phase and group velocities of elastic modes.
