It is shown that Bound States in the Continuum (BSC) exist in an elastic structure consisting of a periodic double array of thin (subwavelength) cylindrical scatterers embedded in a background material, where the distance between the arrays is taken to be large in comparison to both the wavelength and the period of the array. The background medium supports waves with all polarizations, one longitudinal and two transverse, each of which has a different phase velocity. The transverse mode polarized parallel to the cylinders is decoupled from the other two and the corresponding BSCs are similar to those found earlier in the electromagnetic theory. The longitudinal and transverse modes in the plane perpendicular to the array remain coupled, and the corresponding BSCs are shown to exist only for specific distances between the arrays and for specific values of the Bloch phase or ratio of the phase velocities. The latter condition stems from the fact that both the longitudinal and transverse modes acquire different round-trip phases as they propagate between the two arrays. An analytic form of such BSCs is obtained by solving the Lippmann–Schwinger equation in the dipole approximation with arbitrary mass densities and Lamé coefficients.

结果表明，连续体（BSC）中的束缚态存在于一种弹性结构中，该弹性结构由嵌入背景材料中的细（亚波长）圆柱形散射体的周期性双阵列组成，与之相比，该阵列之间的距离较大阵列的波长和周期。背景介质支持具有所有极化的波，一个极化和两个极化，每个极化具有不同的相速度。平行于圆柱极化的横向模式与其他两个解耦，相应的BSC与电磁理论中较早发现的类似。垂直于阵列的平面中的纵向和横向模式保持耦合，并且示出了相应的BSC仅针对阵列之间的特定距离和针对Bloch相位的特定值或相位速度的比率而存在。后一种情况源于这样的事实，即当纵向模式和横向模式在两个阵列之间传播时，它们会获得不同的往返相位。通过在任意质量密度和Lamé系数的偶极近似中求解Lippmann-Schwinger方程，可以得到此类BSC的解析形式。