Reflection of Rayleigh waves from a mechanical resonator grating

The problem of Rayleigh wave scattering from a set of N chains of closely spaced identical mechanical resonators is considered. The distance between the chains is identical to the half-wavelength of Rayleigh waves at the frequency ω taken to be identical or close to the natural frequency of the chain of resonators with allowance for the associated elasticity. The coefficient of reflection of Rayleigh waves from the diffraction grating specified above is calculated.