Bound States in the Continuum in Elasticity

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